Why AP Varus?
Well the thing is that Varus is really fun champ to play. To make it even more fun, you should try out some different builds, like this one. This is the first AP build for Varus, i tested it 10 times, every time i was top player in team, despite defeat or victory. Really try it out, just for fun.
Why this summoner spells?
People always praise heal on Varus, but healing should not be your job, but supports. Surge on the other han stack perfectly with his AP and AS, and he needs both. His W spell works like Teemos. If you ever played Teemo or Kayle you know what im talking about.
And flash always useful pick.
One little trick: If you duel vs range carry, you should always flash behind him. This way you will cancel his fast auto attacks for second and it might just save you. Do it only when minions near or you will do nothing good.
Well here is the thing: AP Varus is really strong early game, but weak late. Thats why i pick runes for AP over time, that will balance his power over time.