All integrations and devices store their states here, not just core integrations.
Correct.
No. The system log is where errors and warnings are written (config/home-assistant.log)
The Logbook integration displays state changes read from the recorder database. So does the History integration, but in a different way (graphs rather than text).
Yes but no.
If you exclude an entity or domain from the recorder it wont be excluded from the Logbook or History integrations but once the recorder purge time passes (keep_days) there will be no data for the Logbook or History to read from the recorder database. So essentially yes you have excluded them from these integrations too.
If you want to use History or Logbook for an item it must exist in the Recorder database
Yes it is possible. Yes it would prevent them displaying anything.
All of them. Custom ones too, via the Recorder integration.
No it is not. It’s a package deal. See: