1) Bad problems vary. The bad thing about that is you don't know what you'll get sometimes. The good thing is that there's nothing super notorious to go wrong on a GC that you may as well write out a check for now. The most common thing that I know of is the exhaust manifold getting a crack which people wind up using as an excuse to buy an aftermarket one with better flow. Depending on the options in it, it may have another potential problem, but that will depend on the drivetrain. I know people love to replace the Quadra-Trac transfer case for the Selec-Trac (Quadra will only have 4 hi, 4 low, and neutral on the shifter. Selec will have 2wd, 4 all time, 4 hi, 4 low, and neutral I believe) but it's a pretty simple swap if you're at all tool-savy. I'm not exactly sure of what the problems are, as I'm closing on 170k with the Quadra-trac with no problems.
2) The typical V8 is the 5.2 liter engine. There's also a 5.9 out there, but that's pretty rare to find. Either would haul a trailer without much trouble if it's in good mechanical condition (just like any engine).
3) I love how mine tows is the best I can tell you. The suspension on GC's are the best on the road, in my opinion.
4) There are manuals out there, but like the 5.9 liter engine, you're gonna have a time finding one.
5) Mechanically, Laredo and Limited are typically the same. The Laredo could also have the inline 6 engine as opposed to the V8, which makes it almost an entirely different vehicle, but a Laredo with the V8 option is pretty much a Limited mechanically. The Limited also has some standard features like the navigational consol thing and the vehicle information screen that the Laredo has to have added on as an option that makes the Limited worth tracking down to me. The navigational consol is overhead and will show various things like temp and direction or mpg, the information screen is easy to find...when you start the engine, it'll tell you how many more miles until it needs service.
6) Averagely, I'd say about 16 mpg. When I'm maintaining speed, I usually get about 21-22 mpg. But with town driving and highway driving, 16.1 is what my system tells me I'm getting.
7) I'm assuming you're asking if it's ok to lift. I'll just say this: It's a Jeep. Of course it's ok to lift!
But more seriously, I'd say you can lift to about a max of 6". Anything more is getting pretty unsafe.
8) It has solids. While that sounds archaic, the GC makes them work amazingly well for some reason. I'm not sure of the size of wheel you can mount on it, so I'll leave that for someone else.
9) Again not my area. I believe 31's will rub under stock suspension, but don't take my word for it.
I could also be wrong about just about anything I just told you, so don't take my word for law. That's just what I know to the best of my knowledge.