I'm going to ask a moderately mentally handicapped (and possibly gay) classmate to stop certain things
That feels very inconsiderate. Why would you restrict them of doing something?
He takes pictures of himself every 5 minutes, he brings weird stuff to school sometimes, and all he really wants is to be left alone
And how does this disrupt you? If it doesn't then leave it alone.
I feel bad for him and want to help him.
I don't think that you will be helping him by restricting him to do things that you find weird. If you genuinely care about him, you can help him by talking to him and being his friend. But unless he is actively harming someone and being disruptive, I don't think I would recommend you asking him to stop doing what he's doing.