1) Yes
2) No
3) Yes
4) No, on the contrary
I did not believe that a sub could improve the overall sound untill I got one, a REL Strata III. All recordings tend to benefit from the addition of a sub, classical and Jazz music actually benefits a lot more compared to Rock and Pop. One of the advantages of a sub is that it will give you the low end resolution at almost half the volume you are used to listening at.
I will not say that REL is the best (have not heard everyone out there) but it certainly should be on the top of your list when you consider a sub.
The biggest problem with subs is that you will never know how good or bad it sounds until you have it in YOUR system and YOUR own room. For smaller rooms, it is generally a good idea to go for a sealed one rather than ported one, to avoid boominess. I have heard similar subs in different systems and they all sound different in different rooms and different systems.
For music the sub needs to be fine-tuned to match seamlessly with the main speakers. In order to avoid the midbass hump the sub needs to be well under the main speakers low frequency roll off and not overlap it.
Just because one has paid for a subwoofer, does not mean it should be in the limelight! Basically, the sub should tell you I AM NOT THERE, it should disappear. SUBTLE is the keyword here!
Depending on your room size, your preference, taste in music, volumes to be achieved, it will take a while before the sub is seamlessly integrated into your system. Many folks expect the sub to start performing at its best the moment it is hooked up to the system and get frustrated, PATIENCE is again a keyword here.