Wow! Lots of questions. Lets take them one at a time.

What does the "U" mean in RG6U?

I have no idea. Somebody said that it meant "underground" but I don't think that's true. If it were you would notice it because the cable would be flooded with grease or goop under the jacket. Apparently it is a vestage of the original mil spec designation and anything with it I wouldn't want to use because it probably doesn't meet the requirements for the stuff we do today. If you have an example post the link, I would be interested in seeing who is selling RG-6U.

Can the same F type crimp connectors be used on RG6, RG6U RG6 Quad shield?

The difference in the outside diameter of the cable means that you need to use the connector designed for that cable and the companion crimper. There are some exceptions however such as the Gilbert USA line that will work with all RG-6.

Must I use 75 ohm terminating resistors on unused splitter ports?

You don't have to but it is good practice to do so. Terminating unused ports keeps leakage to a minimum which is something you should be aware of.

When looking into a piece of coax terminated in an F connector, must the inner, white dielectric be flush with the bottom or can in be back 1 or 2 millimeters? I sometimes can't push the cable in deep enough.

The dielectric must be flush with the bottom of the connecter. If it is too short you are not stripping the cable properly or the shield is bunching up under the jacket when you push the connector on. Keep in mind too that not all "strippers" will strip to the proper dimensions.

Is this true about coax connectors, basically the center conductor must never come in contact with the shield or connector and the connector must be crimped on top of the folded back outer shield so they are electrically common?

If the shield comes in contact with the center conductor the cable will be shorted. Most connectors require the braid to be folded back over the jacket to ensure continuity and minimize leakage. Otherwise the shield will bunch up and just be pushed back under the jacket not making good contact with the connector.

Can I "nest" splitters? Say there's a 4way now, 1 incoming and 4 coax leaving, but I want to add a 5th coax run. Can I remove one of the 4 exiting cables, add a small jumper to a 3way splitter, reattach the original cable to 1 port and my new cable to the other?

Sure. Matter of fact all splitters are multiples of 2 way's in one can.

I have found 4 way splitters, (1 in, 4 out) but no 5 way. Is there such a thing?

I havent seen one. How about a 3 and two 2's?

At what point is a passive splitter not the answer and you need a amplified type splitter.

When the signal level at each set drops below 0db.

I wire houses, and am getting into home entertainment systems, are their any tutorials on the web for the best practices when installing TV coax?

Not that I know of. Best teacher is experience. I always recommend that someone in your position works for someone who does this for awhile. Ther is a lot to learn.

Are there any inexpensive coax testers to validate my installation before the home owner plugs in their TV and receives no signal?

No, there aren't any VOM type testers. Signal level meters require some knowledge of CATV, frequencies and system operation to be useful.

-Hal