I am a new owner of a -SW, and I think I got a great deal. I also got to fly a CTLS It has some quirks but I think most airplanes do. Not all my answers will be totally accurate since I'm a newbie at this, but this was my experience:
1. I had a local mechanic do a pre-buy. He was not a CT expert but he had experience working with the Rotax 912, and had worked on a few other light sport aircraft. The plane also had detailed write ups from Rex Johnson, and some expensive maintenance items completed: a Rotax Rubber Change, and a Parachute Repack in the last year. The airplane was also regularly flown, and run primarily on ethanol-free auto gas. I looked at 2-3 other aircraft. The others were terrible in comparison. Shoddy logs or damage history, the price wasn't right, or they were experimental (Not a dealbreaker, but it brought up concerns).
2. Can't answer #2 but there are a few places you can travel to to get CTLS training. There is one in Arizona (Copper City Aviation), I took some training at a flight school in Colorado Springs as well. If you plan to spend that much it's worth flying somewhere to get it. There may be many more options in NorCal but I don't know of them. The time to start getting transition training is now. That way when you purchase your plane you can fly it home, without being tempted to make bad decisions.
3. These may not be common gotchas but they were mine: I seem to have a lot of electrical gremlins. They are easy to fix, and not safety-of-flight issues, but for example the engine reading oil pressure PSI when it's on the ground and the engine is cold. Or random (Once in a blue moon) CHT alarms seconds after starting that self-clear, or alternator noise in the headsets- things like that. A lot of these are grounding issues or loose connections. From my light research they seem to be common, and easily fixed.
Bigger gotchas are- does the plane look level on a flat surface (might indicate bent gear if it's aluminum). Check the logs. Does the engine have the 2000hr TBO extension? Is there any composite damage or signs of delamination? Any flat spots on the tires? What's the history? Was it hangared?
Lastly: When you go look at the plane, get the cowling off. Do the hoses look cracked? Are there areas where they look squeezed? Any wires loose? Does anything look off?
Random gotcha- more of a post-buy thing, but if you bounce a go-around, even gently, the landing gear has a tendency to vibrate a bit. It doesn't mean it's damaged or that you're a bad pilot, but it's a light aircraft and much different than a C172 or Diamond, and the first time it will raise your heart rate a bit. You really need to slow down on final. It will also kick your a** in turbulence. The plane will handle it fine, but you may not. In exchange for the sacrifice calm days are incredible, these planes are so maneuverable and fun to fly.
4. I have the D100 and it is a great system. In the center console I have a Garmin 796, which has XM weather and all the goodies. I also have the Trutrak linked up to it which is a great luxury. It seems like there are a wide variation of GPS systems installed, and some owners have upgraded them. I would strongly insist you find a plane with an AP. One downside to the Garmin is that they charge like $100-200 a year to keep the database up to date, while I've heard Dynon is free.
5. My -SW has like a 600LB useful load. The LS's with the Skyview have a bit less. Not saying you shouldn't do your W&B by the book, and you definitely should avoid egregiously loading the plane, but it will still climb at 500 FPM with two large adults, full fuel, and baggage. These planes are in a whole other class than standard aircraft, and with only me and half fuel I'm regularly seeing 800-1000FPM at 4000ft. elevation. It smokes the old 172s and Cherokees I used to fly.