I would use "for me" + infinitive in the first two cases: Is it alright for me to come here? Is it OK for me to come here? because they refer to getting permission to do something (in the future), but for the last case, I think it might be asking about something that has already happened, Do you mind that I came here?

Is it ALRIGHT THAT I came here? Is it okay THAT I came here? "Do you mind me coming here" is correct.

Just a small change to the first two questions. The third question is ok. They all mean the same thing. Is it all right for me to come here? / Is it okay for me to come here? Do you mind me coming here?