It’s dose. So you get a higher dose the longer you are exposed. A smaller dose infected less cells are initially infected and maybe you get less sick. Higher dose may mean you get more sick.
Making strong guarantees that people will become immune and won't be infected is part of what makes coming up with a vaccine hard. It's apparently pretty easy and quick to come up with vaccine candidates.
Yes. In some cases, the wrong kind of immune response can cause antibody-dependent enhancement (https://en.wikipedia.org/wiki/Antibody-dependent_enhancement), where the immune reaction enhances the severity of the virus.
This is not terribly common, but alas this exact mechanism has been seen in earlier work on SARS.