Mummyof2Girlies - re-read your op as if someone else had written it. You describe an ex who, sees his child regularly, contributes time and money, and takes a full interest in her education.
That's actually a flattering description of an ex.
You also say he's a pain in the butt and is sarcastic to you. The sarcasm, undermining comments are not on. If contact is troubled, would it be helpful to do handover through a third person? Minimise your contact with him?
And as for your dd wanting to spend time with him, she's just a little girl and I'm sure that she in no way says these things to make you feel bad. Think how much worse it would be if you had to hand her over and she screamed and cried. It is actually quite special that your dd has 2 parents who adore her.
Not sure what to make of your concern that he "spoils" her as you haven't provided detail, but in any case there isn't a lot you can do. It's tricky parenting alongside an ex, isn't it.
But the school thing, well, maybe try to take it at face value. He's taking an interest in her education and that is v positive. It doesn't need to be a competition between you both.
It does sound as though you need to reduce your contact with him as much as possible so you don't keep getting upset by his behaviour.