Buy a used high end phone. 300 € is more than enough, should get you a <2 year old flagship.

But if you want to explore the “real deal” obviously buy used.

1. Smartphone. They do all the image processing, including HDR with multiple pictures etc.
2. Smartphone.
3. a) Smartphone
4. b) impossible
5. Any camera that has a high score in DXOmark “sport”.
6. Essentially anything if you treat it well. Otherwise smartphone (water/dust/sand tight).
7. DSLRs from 10 years ago can do 1080p. So unless you go really old: no problem.