Well, not having a drill press myself...
1. I have been drilling 10mm holes for tuners with a hand electric drill using a brad point drill and centre punching the location for the point. Holes turned out very neat (after I remembered to clamp wood against the rear side to prevent splintering on breakthrough )
2. I think you are right, you need a drill press if you're not using the router for the whole thing
3. I drilled the post holes for my stop tail piece with a hand drill. Haven't tried a bridge that needs post holes yet.
4. They are only small holes aren't they? I would try a hand drill.
5. I did small dots in rosewood using a brad point drill. Had to real careful to only just let the full diameter start cutting, then stop immediately. Worked well though. One that I cut a bit deep, I just didn't push the dot all the way in, let the glue set well before sanding. No probs.
One last thing, for very light work (like 4. above) you can buy a cheap "drill press" frame that clamps a hand electric drill into the frame and let's you lower it with a lever just like a real drill press. I am not suggesting it as a real substitute, but maybe something to help until you get one. I have one, but haven't needed to use it yet on a guitar. But then, I am only a beginner.