You are welcome anytime my friend. Am an old member on this forums but it has been really a long time since I logged in. I have my periods when am active and some periods when am not. Now let me tell you English is not my native language so any time you sense from my answer that I didn't answer you please let me know.
With reference to the Holy Qur'an or Hadiths what makes Muhammad special or different from other Messengers?
Let me start by defining Islam. There is a big misconception even among muslims regarding the starting time of islam. Many tend to think that islam began with Muhammad peace be upon him. That is not true. The first muslim to be on this world is Adam for he believed in God alone and that is the essence of Islam.
From the first person to put his foot on earth ( Adam who was a muslim) till prophet Muhammad peace be upon him there is believed to have been about 120 000 prophets who were having the same concept about who God is and they were worshiping Him alone.
This explains how God chose to deliver for us the message or the way in which we had to live our lives. He chose messengers and prophets among us for them to share his message. He gave messengers revelations and he gave them miracles by his Will to prove to the people at their time that they are really receiving revelations from God. Miracles were like a support for their argument. In that way, people see the signs that would stimulate their minds and invite them to really give it a thought. Is God really there? Did he really send us revelations through messengers? and questions like that.
What is different about prophet Muhammad peace be upon him is that he was sent for the whole world as I previously quoted from the Quraan. In addition, and the most important difference is that Muhammad peace be upon him is the last messenger in Islam.
33:40
Muhammad is not the father of [any] one of your men, but [he is] the Messenger of Allah and last of the prophets. And ever is Allah, of all things, Knowing.
The fact that Quraan says that Muhammad peace be upon him is the last messenger means that the message of islam is now complete, and Quraan confirms that
5:3
Prohibited to you are dead animals, blood, the flesh of swine, and that which has been dedicated to other than Allah, and [those animals] killed by strangling or by a violent blow or by a head-long fall or by the goring of horns, and those from which a wild animal has eaten, except what you [are able to] slaughter [before its death], and those which are sacrificed on stone altars, and [prohibited is] that you seek decision through divining arrows. That is grave disobedience. This day those who disbelieve have despaired of [defeating] your religion; so fear them not, but fear Me. This day I have perfected for you your religion and completed My favor upon you and have approved for you Islam as religion. But whoever is forced by severe hunger with no inclination to sin - then indeed, Allah is Forgiving and Merciful.
But the real question arises here is that messengers at their times were given miracles to prove that they are really messengers. If Muhammad peace be upon him was sent for us, than what is the miracle that would be a sign for that. The answer is the Quraan. ( He also had other miracles that were meant for the people at his times)
What of the Gospel of Christ and the Holy book of the Christians and Jews? Is Muhammad mentioned?
We believe Jesus peace be upon him was a messenger of God and we believe he received a revelation called Injeel. However we believe that this injeel wasn't preserved as it was and is different from the bible we see today. Our view of the bible is that it contains some truth however there are many personal views attached to it. So we don't accept it to be the word of God. The bible we see today is not the same Injeel Quraan talks about. There are many additions, subtractions, and replacement. Even implicit statements are made to say somethings that are meant to.
Nevertheless some scholars to believe that there are some texts or expressions that refer to prophet Muhammad peace be upon him. And as muslims we do believe that each holy scripture foretold that there are messenger coming after and described them so that people would follow.
They quote John 16:7-8
7 Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you.
8 And when he is come, he will reprove the world of sin, and of righteousness, and of judgment.
Some muslims say these verses are referring to the prophet Muhammad peace be upon him. Majority of christians to my knowledge say that this refers to the holy ghost.
Another verse is Isaiah 29: 12
"And the book is delivered to him that is not learned, saying, Read this, I pray thee: and he saith, I am not learned."
They explain that verse to be referring to Muhammad peace be upon him because the first word of the holy Quraan to be revealed to our prophet through the angel Gabriel was "read". The prophet replied I am not a reader.
In the hadeeth in as-Saheehayn from ‘Aa’ishah (may Allah be pleased with her), she says: … (This went on) until the truth came to him when he was in the cave of Hiraa’. The angel came and said, “Read (or recite)!” He (the Messenger of Allah (peace and blessings of Allah be upon him)) said: “I said: ‘I am not a reader.’ Then he took hold of me and squeezed me until I could not bear it any more, then he released me and said, ‘Read!’ I said, ‘I am not a reader.’ He took hold of me and squeezed me a second time until I could not bear it any more, then he released me and said, ‘Read!’ I said, ‘I am not a reader.’ He took hold of me and squeezed me a third time until I could not bear it any more, then he released me and said: ‘Read! In the Name of your Lord Who has created (all that exists) … He has taught man that which he knew not.’ [al-‘Alaq 96:1-5].”
Some muslims even go further by saying that the name of Muhammad peace be upon him was mentioned in the song of solomon 5:16 but I didn't do my research on that.
Of course whether these links are perceived to be reasonable or not is subject to each person. In my opinion these are interesting points to look at, but the fact that we see the bible different from the Injeel that was revealed to our prophet Jesus peace be upon him makes this argument of less importance. However, many find that to be fascinating.
As for the holy book of the Jews, similarly we believe in the Torah however similarly to that of the injeel we can't find it in the original form.
3:3
He has sent down upon you, [O Muhammad], the Book in truth, confirming what was before it. And He revealed the Torah and the Gospel.
3:4
Before, as guidance for the people. And He revealed the Qur'an. Indeed, those who disbelieve in the verses of Allah will have a severe punishment, and Allah is exalted in Might, the Owner of Retribution.
3: 50
And [I have come] confirming what was before me of the Torah and to make lawful for you some of what was forbidden to you. And I have come to you with a sign from your Lord, so fear Allah and obey me.
There are more verses talking about Torah and Injeel (the gospel)
Is there anything special about Jesus in the Quran or Hadiths that would distinguish Him from any other Messenger or Prophet?
Yes there are many.
Here is a set of verses in particular I would like to highlight talking about the miraculous birth.
19:16-36
16 And mention, [O Muhammad], in the Book [the story of] Mary, when she withdrew from her family to a place toward the east.
17 And she took, in seclusion from them, a screen. Then We sent to her Our Angel, and he represented himself to her as a well-proportioned man.
18 She said, "Indeed, I seek refuge in the Most Merciful from you, [so leave me], if you should be fearing of Allah ."
19 He said, "I am only the messenger of your Lord to give you [news of] a pure boy."
20 She said, "How can I have a boy while no man has touched me and I have not been unchaste?"
21 He said, "Thus [it will be]; your Lord says, 'It is easy for Me, and We will make him a sign to the people and a mercy from Us. And it is a matter [already] decreed.' "
22 So she conceived him, and she withdrew with him to a remote place.
23 And the pains of childbirth drove her to the trunk of a palm tree. She said, "Oh, I wish I had died before this and was in oblivion, forgotten."
24 But he called her from below her, "Do not grieve; your Lord has provided beneath you a stream.
25 And shake toward you the trunk of the palm tree; it will drop upon you ripe, fresh dates.
26 So eat and drink and be contented. And if you see from among humanity anyone, say, 'Indeed, I have vowed to the Most Merciful abstention, so I will not speak today to [any] man.' "
27 Then she brought him to her people, carrying him. They said, "O Mary, you have certainly done a thing unprecedented.
28 O sister of Aaron, your father was not a man of evil, nor was your mother unchaste."
29 So she pointed to him. They said, "How can we speak to one who is in the cradle a child?"
30 [Jesus] said, "Indeed, I am the servant of Allah . He has given me the Scripture and made me a prophet.
31 And He has made me blessed wherever I am and has enjoined upon me prayer and zakah as long as I remain alive
32 And [made me] dutiful to my mother, and He has not made me a wretched tyrant.
33 And peace is on me the day I was born and the day I will die and the day I am raised alive."
34 That is Jesus, the son of Mary - the word of truth about which they are in dispute.
35 It is not [befitting] for Allah to take a son; exalted is He! When He decrees an affair, He only says to it, "Be," and it is.
36 [Jesus said], "And indeed, Allah is my Lord and your Lord, so worship Him. That is a straight path."
Here is a link for a comprehensive listing of the verses talking about Jesus peace be upon him if you like
https://www.namb.net/apologetics-bl...to-jesus-isa-in-the-qur-an/?pageid=8589953017