Answers, so you can tell me if I was cheating. >:)

1. Breaking a statue forces two kids' parents to close their shop. And results in one of the kids being transformed into a goblin. -- Magical Shopping Arcade Abenobashi
2. Schoolgirl suffers from PTSD after being forced to participate in after-school activities involving rollerskates and weird hats. -- Alien 9
3. Young girl's physically violent love interest stalks her at school and appears in her bedroom without warning. When she's forced to accompany him on a cross-country bike trip, her grandfather lies to the authorities about her whereabouts. -- Inu Yasha
4. A young girl works in the sewers for a company with ill-defined goals. She's killed almost immediately. -- Excel Saga (I thought 'ill-defined' would be a dead giveaway)
6. Foreign customer service representative forces a girl to go to insane lengths to reclaim a package accidentally consigned to his organization. To his amazement, his final offer that she should marry him instead is rejected. -- Labyrinth
7. Nothing happens. Everybody dies. But the hero has luck on his side, and it all works out in the end. -- Neverending Story
8. Failing to deal with an infestation of rodents causes a man's home to be demolished. He eventually finds a new home living in a cave in the wilderness. -- The Hitchhiker's Guide to the Galaxy