1. I haven't designed a theater yet (no budget), but if I were in the market, I would definitely use HDMI for my projector run.
2.
a. As I said, I don't have a need for it yet, but it would be determined by the room size. Probably somewhere around 10m.
b. N/A
c. I could forsee needing a 50ft cable in a giant theater room (one can dream, can't he?).
3. If I were designing a room, everything would be in conduit. EVERYTHING. So yes, I would need to pull my video cable through conduit. The termination size wouldn't really be an issue, because I would run at least a 2" conduit to my projector, if not larger.
4. Ooh, that's a toughie. In my personal case, it was around 7%. I'd say that's pretty reasonable. Obviously it would be more if I were dropping a few hundred on a long video run in addition to other cabling. I'd say max 10%. If you can't get what you need at this point, you're spending too much money somewhere.