Yes it is.
Thank you.
No it doesn't.
Depends on the quality. If it's well written and well thought out, I like fanfiction. If there are gratuitous spelling and grammar mistakes, I really can't forgive someone not using spellcheck. I do love when somebody does something new and inventive with characters I already love. Case in point:
Bleedman. He does GORGEOUS webcomics about my favorite cartoon shows when I was a kid, and his stories are imaginative and captivating. Check out his stuff:
The Powerpuff Girls Doujinshi (it's actually a lot less girly than it sounds. Features a HUGE cast of old CN and some Nick shows.)
Grim Tales From Down Below takes a much darker look at Grim+Mandy's (from the Grim Adventures of Billy+Mandy) world after they have kids. My personal favorite. And finally, his own original work, with original characters:
Suger Bits. Currently Sugar Bits and Grim Tales are updating, but check them all out for some gorgeous archives. (/rant)