Boy, you don't ask easy questions.
1. an alternative is using home & end. Don't know about remapping, but it should be possible.
2. I always had random times with RSRD. Though I haven't really played in a while, just some testing, so that may have changed as of late. Don't know how to change this yourself.
3. I always figured the crew staying on the bridge was to "simulate" the time it took for all hands to get below. Guess it depends on your point of view.
4. Yeah, that's pretty weird. IIRC it doesn't happen if you're below PD and go deeper. No fix that I know of.
5. Clock is a total mystery to me, never really payed attention to it. Although, as far as I can remember it presents local time. Maybe you haven't been through enough timezones?
Less then helpfull, but at least it's an answer.