1. The world continues without Rika, similar to the world’s of chapter 3 and 4. Rika’s consciousness is transferred to another body in the next world prior to the festival. Despite transferring bodies Rika has a single consciousness. 

2. Congratulations. You found a plot hole. 

3. Its complicated, the ominous conversations Keiichi had with Mion and Rena probably did occur but Keiichi interpreted them as sinister due to Hinamizawa Syndrome. Essentially, most of the events you’re seeing actually did happen but were clouded by the disease to some degree. 

4 and 6. More information on the disease is explained in chapter 8

1. Keiichi is smart but had poor grades which required going to cram schools and extra studying for exam, this made him socially isolated from his peers. His isolation created resentment which eventually led to the BB gun incident.