All I can say is that there is no real evidence due to distortion in historical facts (and that because the Hikayat Hang Tuah was authored by the influence of the British! -as it is even mentioned by the link you gave that it has contradictions to Sejarah Melayu itself) to prove but some basic common sense and deep thinking on the events will answer the question.
Firstly, the usage of 'Hang' in those days were common. There are many names that had been virtually 'lost' and never used anymore in this generation due to higher Islamic influences and usage of Arabic names.
'Hang' can be a sort of reference of a particular person's title or social status (as suggested by your reference that it was a surname given by the Chinese Emperor, but I find this rather inaccurate), particularly at the 14th/15th century Malaccan language. It is more like Seri, Sri, Si and Sang.
From the knowledge I've acquired in acient Southeast Asian history (from my family knowledge and old texts), such names were popular and you can just search them in any old books. 'Hang' is said to be used in reference to a person of 'higher' or 'equal' class to those of 'Sang' whereas those of 'Seri, Sri and Si' are of higher classes (more like the old Indian system of social classes, which runs from Brahmins, Kshatriyas, Vaishayas, Shudras).
I don't deny this idea as there was a high vedic influence in the old Malay civilisation during the pre-conversion days of the Malays to Islam and Parameswara, by the way, is also an Indian name, derived from one of the many names of Lord Shiva. Legend has it that Parameswara is the descendent of Alexander the Great, suggesting that his ancestry origins may be of Indo-Greek during the expansion of the Alexandrite empire to India.
So, to answer your question, were Hang Tuah and Hang Jebat actually Chinese? In my honest opinion, they were in fact JAVANESE, sent by the Majapahit empire as servants to the Malaccan kingdom out of goodwill and to enhance relationship ties and also a form of protection to the Sultan as they were under threat by the Siamese (for some stupid things they did previously such as killing a prince and other forms of betrayals... they asked for it).
The theory that suggests Hang Li Po a court official's daughter or a palace servant is highly possible as the Chinese had tricked many smaller kingdoms into believing this and kept this as a way to prolong/retain their family honour/status as giving away their child to a kingdom of lower status is deemed derogatory therefore, the idea of the title 'Hang' is more suitable for Li Po is she was indeed of a lower status/palace maiden.
I cannot ascertain for the origins of Hang Li Po but the name Li Po suggests that she is indeed of Chinese origin and 'Hang' was merely a title rather than her actual name (as earlier suggested). According to studies, Sultan Mansur Shah married to her and it was meant to strength ties with China as a further assurance of safety from Siamese attacks (another debatable subject, but it does make more sense to think about the Siamese being in constant engagement of battles in order to reclaim parts of 'lost' territories and re-establishments/reunification of their war-torn kindgom at that time as result of the Burmese invasions, when the southern territories (particularly the Pattani kingdom, which was a very prominent key ally to Malacca) had betrayed the Sukhothai and Ayutthayan empires).
In reference to your link, it was an excellent write up, yet I still find that some 'facts' given are questionable like the DNA testing and so forth. Another problem with this research is that it may be done so out of pro-Chinese sentiments (which has been traditionally included in debates and among the things that people say about Hang Tuah is that he was also a Bugis as the name of his mother and other physical description and behaviour traits ---The Chinese are trying to prove this to say that the Malaccan kingdom owed their allegiances to Admiral Zheng He for his aide in the establishment of Malacca as an entreport which links the Maritime trade industry of the east and west and without the help of the Chinese, they were 'nothing').
To date, several 'DNA' tests were said to have 'proven' that Hang Tuah & the geng were Chinese, Bugis, Javanese and others. Worse, there were also claims that the Mausoleum of Hang Tuah do not contain any physical remains but merely a symbolic site! According to legend, Hang Tuah retired from his service with the sultan and had lived in Mount Ophir/Gunung Ledang. Some mystics even claim that he is still alive and there were rare 'sightings' of him on several events.
I did not make this up and you can confirm this through various sources and write ups/journals. This is just the story of Hang Tuah excluding the origin of the famous Keris Taming Sari, which is also another claim/proof by some to link him to his Javanese origins (the Keris is a Southeast Asian/Indian weapon and was never used by the Chinese ---why would highly trained warriors give up to their expertise in their weapon to a foreign weapon, in those days?).
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The story of Taming Sari was said to be of Javanese origin, and the original owner was a warrior named Taming Sari, hence the origin of the name of the model of the Keris (which was unique and said to be extremely potent), of which later became the possession of Hang Tuah.
Keris Taming Sari was known among the old Malay warriors as 'Keris Derhaka' (Keris of betrayal) as warriors of that time fought among one another to gain ownership of that particular weapon. Hang Tuah fought Taming Sari as one of the tests and challenges of a warrior (in those days, honour duels were very commonly held and it was a matter of life and death -the victor keeps the weapon of his/her opponent as an act of honour for the deceased as the weapon had been faithful to its owner till his last breath... ever wondered why the warriors or descendents of warriors kept the numerous kerises left behind by their forefathers? Here is also your answer...).
The idea brought up by some that suggested about the execution of Hang Jebat for betraying the sultan by having an affair with one of the palace dayangs (maidens) was also rediculous as a man of such honour will never condone such practices and lead to his own downfall of status and in those days, the pride of a warrior was often kept in high esteem.
It would make more sense to think that the battle between Hang Tuah and Hang Jebat was linked to this keris (Taming Sari) and that was why Hang Tuah had decided to get rid of it after defeating Hang Jebat as it has brought betrayal to a close and dear friend of his through conspiracies and other forms scandalous accusations. To a warrior, there is no other better way than to die in honour while in battle and Hang Jebat had proven this by giving himself in to Tuah out of love and respect as Tuah was more like an 'elder brother' to him and had saved him throughout their many adventures before serving the sultan.
There is also a lot of mystical aspect in this duel. According to legend, Tuah swapped the keris of Taming Sari with the keris Majapahit (which both Jebat and Tuah were invincible to), that resembled the Taming Sari as he did not want to kill Jebat intentionally (both were said to be invincible to weapons and yet, were not invincible to the potent of Taming Sari's powers). This feat of invincibility also work along with the power of one's perception of reality and faith. After days of duelling one another, suddenly Jebat was confident that the keris used by Tuah is a Taming Sari and thought that he had already acquired invincibility to the Taming Sari. Within a blink of an eye, that perception had brought Jebat to lose his concentration and also 'powers' of invincibility thus stabbed by Tuah.
I shall not elaborate with too much details about kerises as it will eventually lead to other subjects. I hope that this answer is sufficient and informative, and had served its purpose.
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You asked if the Chinese helped established Malay sultanate of Melaka and if Chinese presence was actually more crucial for Malayan history than taught in schools?
My answer is a whole hearted YES and ABSOLUTELY. As I have mentioned, it was the role of the Chinese who helped bringing in outside traders from other port/Maritime kingdoms around the region, more like today's stockbrokers and business people (they've never changed much, if I this was the right way to call it). They had been one of the greatest contributors alongside with the Indians and Arab traders.
You are right about your theory with regards to the weaponary skills of fighters. Most warriors do learn to adapt and so forth. However, this argument is very vague and as I've told you, it would be wrong to jump to any conclusions.
Throughout my encounters with legends of this old man, there were numerous claims that he was also a Bugis, which I also find it highly possible.
I shall not continue trying to prove or disaprove whatever Tuah's origins are. As I have given my answer to you, it is also up to others to come to their own discretion (yet, no one can come with any real conclusions... its just too vague to know... eventhough I can tell you that my sources are reliable but its still questionable as it came from my Javanese teachers... but you know how it goes... everyone wants to claim him as their own ---including the Chinese)...
Your theory on the possibility of him being a Chinese (or possibly mixed) is also quite an interesting question and honestly, I would like to leave it to the others to make their own discretion. It is definitely a possibility, no doubt.
The idea you gave on the Saqalib soldiers were examples of how warriors fought in a very different region, where there is very little relevance to the military culture of Southeast Asia. Over this part of the world, in the old days, warriors never disguise themselves as locals if they were sent by another government. One way I can example that I can relate to this is; even the Japanese warriors were in their Samurai armours while battling the Burmese for the Ayutthayan soldiers under the establishment of King Naresuan (you can watch this in the most recent movie being made... though some parts are fictional/mythical, most of those events taken place were of historical sense, based on old Ayutthayan documents ---this was about the same time as the Malaccan establishment). They did this in order to keep their numbers in count during battle and may send for reinforcement at any given time if they are in need. Also, this is one way for the 'host' generals to determine the efficacy of their import soldiers and not getting confused with the dead as they may be of similar looking ones with his own/opposition men. Another way to determine this is to look at old paintings of the different group of warriors who fought alongside, including foreign 'imports' for their battalion.
'Hang' is/was never a Malay word... as I have given my example of how it is being used, I suggest you should understand better by now, it is an old word/name that has virtually 'lost' its usage. There are many old Malay names and words that has been 'lost' today through adaptation and absorption of cultures and other languages. (By the way, what is 'Malay' to you? Malays never had a culture or language of their own anyway... its all about imports, if you know what I mean). Their identity is never clear and many things claimed to be 'Malay' is especially new and in fact, historically incorrect.
Many of their 'adat resam' today are the result of intermarriages and cross cultural adaptation, predominantly from the Hindu aspects and this is highly evident in weddings, funerals and those age old pantang-larangs. Just as you would, I too, challenge to their Ketuanan Melayu doctrine as it is nothing more than a political ploy to gain supremacy in society.