It looks like most of your questions have been answered, and the link to the tickets thread has lots of good help. Just be advised (At least the last time I looked) it hadn't been updated in a while.
2.) AP's allow hopping. they also give some other perks. I suggest you read up, the list is long and complicated.
4.) You can buy AP's that include the water parks- but basic AP's don't include water parks. DO read about converting regular tickets rules!
3. ) Usually yes, but as another poster said- some room discount offers are packages that include tickets. Then, as an AP holder, you are eligible for AP discounts. Once upon a time they were big and early, but these days the AP discounts come out late and are often on par with General Public discounts. Sometimes the best deal is to book a GP discount, then switch to the AP discount when it arrives. Usually, if you buy a package that includes discounts- you can later put the cost of those tickets towards another AP. Sometimes you can add
DDP with an AP discount, but it is not usually a discount anymore. (Just a way to lock into prepaid)
Always price out your assorted discount offers to see what works best for your party and touring style. Sometimes one is a better deal, other times they are similar.
Tables in Wonderland might increase your savings if you eat on-property, have a bigger group, and/or like lots of TS dining. If you are just a group of two, and eat QS, it may cost more than it saves. TiW does give a discount at the value food courts though. Also, the discount is not automatic, you have to remember to show the card.
*****TIMING is everything!!!*****
Be aware converting tickets might be relatively quick, or it could be
VERY slow. Basically you can ONLY do it at the parks or DTD- at Guest Services. Generally, it is smart to do it right AFTER using the tickets once to enter the park, but make sure the tickets are not ALL USED, and make sure you don't use any pluses- if you are only buying regular AP's (but your original tickets are pluses. Once you sue pluses, you can only convert your tickets to the plus AP's. Worst time of day to visit GS is morning! Afternoon or evening MUCH better!
It is a roll of the dice. Converting tickets might take 15minutes, or the wait-plus transaction might take an hour plus! In my humble experience, the MK is by far the best place! I've always had great service there. the line at DTD can be very long. (water parks? Maybe?) My least favorite place is Epcot, especially the back entrance of Epcot. AVOID THE IG!
Oh, and if you are going to Universal....Their AP's are a great deal! I converted my two day hoppers for like $15, no hassle at all!