Great post, Sd.
1. Depends upon your monitors' abilities, and of course whether there's any musical programming below their LF performance cutoff.
2. Sufficient? Probably. Will it sound integrated and tight?
Not easy to accomplish.
3. No. Subs are more important for HT special effects. (C'mon, guys, I'm trying to keep it simple here!)
4. Not if it's a good one integrated at a low freq.
Can't stress the importance of knowing what your monitors are doing in your room. Again, oversimplifying, if they're largish 6.5-7" two-ways rather than diminutive 5" there's less need for a sub. If you do try a sub I strongly suggest that you start with FAST ones like the RELs, some Velodynes, and the one I bought, the Boston PV1000 (Vel clone), and start at the lowest crossover frequency, working up until integration is best. And yes, room placement can be key, even more so if it's a cheap, slow sub, which can very easily be worse than no sub at all!
You state that your monitors "go" down to 45-50Hz, but I wonder how many dB they're down in-room? There are some 6.5" two-ways that are surprisingly full-range, but your room-loading has a lot to do with it too. Perhaps you could tell us what your speakers are and room dimensions for more specific advice....