There's clearly a lot of history here, and your subsequent posts make it clear that he is a really difficult man who - appears - to be motivated not by wanting to be a fully involved father, but by the idea of getting one up/over on you. That's shit for you to have to deal with, and I quite understand why you are so upset.
But you are getting upset about some of the early posts. While it is always unacceptable if people are calling you names and I am not trying to excuse that if that's been done, non name calling yet negative responses to your OP have angered you and I just wanted to say the following.
You have to remember that none of us know you. Your situation is so clear to you, because you're living it. You know what you mean. you know the history. But all we know is what you write. Nothing more.
And what you put in your OP described nothing more than a man who sees his child regularly, went to her first day at school, helped pay for her uniform, joined the PTA, wants to be involved with school, wants to take her to events...
and the worst thing you said he does is 'pokes his nose in' (which he's allowed to - it's not 'poking your nose in' to your child's life!) and make sarcastic comments.
now, from your further posts, it is clear there's much more going on here, and you clearly feel he's trying to hurt you and isn't interested in being involved in his child's life, he's just using being involved in it to score points and piss you off, but none of that was described in your OP.
I am really sorry that you've been called names. That is uncalled for and it shouldn't happen.