Muslims arguments against Christianity

I hope this is an ok sub to post this but I've been listening to a lot of Muslim arguments against Christianity & wanted some answers on some things to maybe better my knowledge on both religions....

The Trinity: Muslims seem to always make the argument that God can't be three parts. I've seen some Muslims mock the idea of "God" being born from a human woman or Jesus going hungry etc. Why is the Trinity an argument against Christianity? To me, it's like, well God can do what he wants? I didn't realise there was a rule book for God that he can't be one being split in three persons. Why is it so hard for Muslims to support the trinity exactly?

Another is their religion backed on the story of Prophet Muhammad. Now I don't know Islam to my fullest so I hope not to cause any offence but one thing which has confused me is; they believe in Jesus as a prophet, sent by God, that he had powers to cure the blind and walk on water etc. So Jesus demonstrates God-like powers & even hints at being God in Mark 14: 61-64. But they seem to just move past him as the ultimate prophet & instead primarily focus on someone in a cave who has conversions with an angel, not even God Himself.

I can't comprehend the authority to pass Jesus along as "just another" messenger but look to Muhammad as the last & ultimate Prophet. We know angels can be corrupt for starters. Even Satan was an angel. Plus, why would God operate that sort of conversation with an angel as a middle man. Plus how can we rely on Muhammad, Jesus had visual evidence with his God like actions. Why do Muslims feel so confident in Muhammads words? Without trying to sound offensive at all, could we not argue Muhammad was having some mushroom type hallucinations for 23 years in that cave? Atleast with Jesus we have his God like miracles to go off.