Three things for Eggnivia

Three ideas for our favorite frozen phoenix:

Increase base mana per level

One of the trademark traits of Anivia, and one weakness that should be conserved, is her incredible mana hunger. However, in light of the recent nerfs to mana regeneration, that weakness was made a little worse than it should be. To alleviate this, I'd like Riot to think about increasing her base mana pool somewhat, to make Athene's a little more efficient on her.

The wall from Crystallize applies the "Chilled" Debuff for champions dashing through it

For 1.5 seconds or so. Helps against assassin's and other suckers who dash through your wall to kill you, but doesn't punish people for escaping over the wall with a dash.

Increase Glacial Storm's earlier CDs a little, but have it begin to tick down after the first cast

One problem for Anivia nowadays is the mobile nature of big fights that makes her ultimate a little underwhelming. By allowing its CD to tick from the first cast, she's less punished for wanting to reposition it. If Riot wants to keep a certain deal of time between deactivating and recasting, one should consider adding a static, 2 seconds cooldown between those two actions.

Would these ideas retain her high skill floor nature, but benefit her in today's League? Or are they too much and would make her overwhelming?

P.S.: The most important buff she needs, however, is the readding of "Eggnivia" in the chat box if she's writing while egged. That removal was a serious and almost champion-breaking nerf.