1. Will installing watercooling, and thus lowering the temp. of my comp. also lower the amount of heat the computer puts out, thus allowing the room to be cooler?
No, your computer will produce the same amount of heat, the room will be no cooler or hotter after a few minutes of operation. (it make take a few minutes for an equilibrium, for each part to reach it's regular running temp). Well in theory there might be a trivial difference in the amount of heat a water pump produces versus heat produced from the fan(s) it would eliminate, but that's insignificant.
IF the ultimate goal is a cooler room, you need a method of removing heat from the room, somewhat similar to a strategy to remove heat from a computer case. As with water cooling to remove heat from a chassis by flow of heated liquid, you "could" just move that heated liquid right on out of the room to an external radiator, but frankly I don't like that option, too much customization and localization, and could be unsightly, quite time consuming, more costly, etc.
The other more obvious solutions to room cooling are active airflow from a fan(s) or air conditioner. Even in winter, computer rooms surrounded by other areas at hospitable temps may require an air conditioner, if a more elaborate, sometimes isolated ductwork to ventilate the room isn't possible.
More significant is whether your water cooling setup (including any fans you might continue using) removes enough heat, fast enough, from other areas of the system. For example, a motherboard needs active airflow unless deliberately designed for very severe environments (_NO_ PC motherboards are designed for this). This is not just an issue of stability but of wear on components like mosfets and especially capacitors.
2. If you use watercooling, is there any point to having a case loaded with fans? Will fans offer any further heat dissipation or are they utterly useless if you have watercooling?
Fan(s) are manditory unless you can accept shorter system lifespan, and you will have to take it upon yourself to measure the temps of everything to determine how hot is "too" hot to achieve the lifespan you need. However, since the water cooling is removing a lot of heat, you can get by with lower airflow, sometimes substantially lower. Whether this means fewer fans or not could depend on where the fans are located, and how it effects noise levels among other things.
For example, if you needed 20 CFM still for best results, running one fan to get it would be significantly louder than 3 fans quite undervolted, but it could easily be that you had a more modern case with a big 120mm rear exhaust fan, and a single fan will still move enough air while remaining quiet.
Maybe you don't care about "best results" though, we can't decide for you how long the system needs to last, nor how much time or expense would be a reasonable tradeoff for you. It would be easy to write that you should design for max lifespan possible, but on the other hand I threw away a bunch of old systems that had sat in my basement for years, lifespan for them wasn't a problem and their stock fans were louder than necessary, but they had lower heat density too, aren't directly comparable.
In short there are many variables involved and we can't make generalizations that would be applicable to any one unique system other than "no", it is not automatic that you can just do away with fans without checking what the result is.
It should also be noted that many people get rid of some fans but not the one in the PSU. PSU can can be just as loud if not moreso if your other parts have good aftermarket heatsinks designed to be low-noise. A system that isn't water cooled can be just as quiet as one that is, given the right case and 'sink choices. Sometimes even quieter, some pumps aren't exactly quiet.