Annie is a bit of a problem child
Everything about her... 0 cast time, short cooldowns, and mana refunds. She has absolutely no downside. Early, she can just CS with her q for absolutely no cost, then when she decides to 2v1 the mid laner and jungler (when not even slightly fed) she can go ahead and back and get her items. When she reutrns to lane, her ulti is up again (because why not have a next-to-no-cooldown ultimate). Another mage can't even hope to outburst her because of the instant cast time... But it really is mostly her early game. She is waaaay to safe of a pick to be able to just last hit every fucking minion with her q... Refunds all mana cost and halves the cooldown. Really? that doesn't seem a bit OP. You wont miss a single minion and be able to bully your lane opponent with no chance of being ganked every 8 seconds (only using q).. You can't even engage her when she doesn't have a stun... She can just cast her other abilities and have it up.
She is just waaay to strong early and needs some cast times and actual mana costs.
My suggestions: Make her Q a 15/13/11/9/7 second cooldown and 70/80/90/100/110 mana cost and only refresh half the mana cost and cooldown Giver her some casting time, because 3.5k damage in 1.3 seconds is a bit excessive. Then tibbers needs to only last ~15 seconds and be on a 110/100/90 second cooldown Her passive will be every 6 spell casts
That way she has to vamp up a little bit instead of when ever she decides she wants to rape the other team. I really don't think these nerfs will effect her late game, just not let her sh*t all over the lane she is in.
Also, we should remove teemo
Mana refund?