Best band EVER!!!: Given your criteria? God help me, I'd have to say Aerosmith. I can't think of....OOOOH, what about the Rolling Stones?
...I'm not helping myself here, am I? See, your criteria aren't what I'd use to necessarily denote "best". But that's me.
Most Overplayed "Indie" Song EVER!!!: Yeah, this would be an oxymoron. But eh. "Inside Out" by Eve 6. (I hope oneders count as "indie".)
Lamest Idea for an Album Cover....EVER!!!: Sooooooo maaaaaany to choooose from. But I think this one is FTW:

How can you hate this? I mean, he's even got the kickass half finger gloves. And those sunglasses! Lorenzo Lamas, eat your heart out.
Most Adequate guitar solo...EVER!!!: Oh god. What a thing to ask a percussionist. Uh...let's go with the solo from "Dani California" by RHCP. Vanilla solo, vanilla song, blatant ripoff of the Heartbreakers' "Last Dance with Mary Jane". Check, check, and check.
Most Ridiculous Hairstyle on a Rockstar under the age of 30 EVER!!!: Do I pay attention to hairstyles? Geez. Um. I submit anything Pink has ever done to her head in the name of "bein all 3xtr33m j0".
So....yeah.