Well, actually, we do believe Mohammed healed people and performed similar miracles, as all prophets of Allah including Jesus are capable of doing. I wrote a post about miracles somewhere up above.
As to the question of corrupted gospels, I’m not a historian, I just translate things. I know a little bit about the study of ancient documents from having studied a few ancient languages during my degree, but that’s a question for an expert, and I’ll see if I can find you an English book recommendation on tahrif. Maybe start with
Secrets Of Mount Sinai: The Story Of Codex Sinaiticus for some interesting history on the the textual scholarship of the Bible. It’s decently well-written and entertaining, so it shouldn’t be a dull read.
To clarify regarding the Crucifixion, the popular interpretation in Islam is that Jesus was not crucified, but that it was made to appear so.
And [for] their saying, “Indeed, we have killed the Messiah, Jesus, the son of Mary, the messenger of Allah .” And they did not kill him, nor did they crucify him; but [another] was made to resemble him to them. And indeed, those who differ over it are in doubt about it. They have no knowledge of it except the following of assumption. And they did not kill him, for certain. Rather, Allah raised him to Himself. And ever is Allah Exalted in Might and Wise. - Surah 4:157-8
So, not really in conflict with history, there. It’s not saying that people didn’t believe it happened, just that (depending on the interpretation) another person was crucified in place of Jesus having a similar appearance. In classical era Islam, the belief was that even if Jesus was crucified, it did not kill him because he was raised to heaven in defiance of the attempt.
To address the point about how I can just believe that the Koran was dictated to the Prophet (peace be upon him), etc: In part, because I don’t think it would have been possible for a mere person to produce the Koran and do the things that Mohammed (peace be upon him) did without God’s direct guidance. In part because I listen to the opinions of people with credible and authoritative knowledge of the subject and there’s nothing really in the Koran that would suggest to me that it’s false. In part, for experiential reasons. I don’t need for anyone to have seen the angel to believe in the Koran for the same reason I don’t really need for anyone to have seen the angel that spoke to Mary or have seen Moses diligently taking dictation on a stone tablet from a voice in the sky. Just because no one happened to see something happen, doesn’t mean it didn’t happen, one just has to decide from the larger picture how credible the assertion is. So, did you go to Mars? Probably not, but who knows. So, I choose not to believe you, because I’m just not convinced, but I’m ultimately agnostic on the subject of your Marshian journey. In the Message of the Koran, I am convinced. I keep an open mind, I use my best judgement, and I have faith for my own reasons. Allah is perfectly capable of instilling that faith in other people, so I leave that part to Him. ¯_(ツ)_/¯