I've owned and ridden a few. I prefer short wheelbases as well; if I were touring cross-country, I'd probably go with a long wheelbase, but I find the shorties are a bit more sporty.
Specifically:
1) Short wheel base, long wheel base. High racer, mid racer, low racer (fun, but a bit limited visibility). Over-seat steering, under-seat steering, convertible steering. Front wheel drive. The options are endless...
1a) Tight turns are easier with a SWB.
1b) Not a huge difference in practice, really, unless you're talking a lowracer.
1c) Simple and straight chainlines are of course better; that said, LWBs with low botto brackets have chainlines as straight or straighter than the dual-big-wheel highracers.
1d) Center of gravity is lower; not really more or less stable than a regular bike, just different.
2a) It's not really a big issue, once you've become accustomed to the recumbent position. You can't stand, so you're effectively doing repetitive leg presses whilst climbing; gearing down a bit further and spinning is the way to go, generally speaking. The only hill I've not been able to climb on mine is Canton, because I tend to tip back and turn into a unicycle at about 35%.
2b)You've got huge flexibility with gearing, especially in the 'bent world where mountain mechs play nicely with road triples. I'd say a 23"-117" range would be fine for riding around here, and you'll rarely need anything that low.
3) Go to a dealer. Spend an afternoon...seriously. There is so much variation between models that you really need to spend some quality time seeing what fits you. Doing researh in advance is good, but don't be surprised if you find that what works best for you isn't what you expected. I highly recommend Rob at RBR in State College: good guy, and he'll work with you to make sure you get on the right bike.
Gerry Kraynick's a good resource for local 'bents for sale; also, if you'd like to take mine for a spin sometime, or just have me spout off for hours on the subject, PM me or email dan.blumenfeld at gmail.