I read -somewhere- that what social skills dwarves improve upon depends upon their personality. It was something in the wikis, and was documented pretty well with numerical ranges attached to a dwarves listed personality at the bottom. If falling above or below a certain range, certain skills are either available or lost.
Actually, just found it on Wiki, though it's a 40d article. Not sure how much it applies in the current version, but it may very well still be the same :
http://df.magmawiki.com/index.php/40d:Personality_traitYou'll notice some skills, according to that, require particular personality traits to be above or below a certain number.
Also, as far as raising the skills go - if you designate a table to be a dining hall, dwarves will throw parties around it. This can be very bad, since dwarves will spend several months partying - and thus, not working. But it also gives them a chance to make friends/raise social skills. If you want them to stop partying, you can simply cancel the dining hall and they'll all go back to work.
To your second question - certain hard to obtain gems are great to get from caravans (star rubies, star sapphires, diamonds). I always ask for those. Platinum and Aluminum are also nice, though I've yet to see Aluminum anywhere. Any other metal you particularly want but don't have a lot of. Crystal glass is also good, since rock crystals are hard to come by (but can also be ordered as gems through the caravan to make even more crystal glass). Finally, if your fort doesn't have gypsum, bags of plaster powder area also good things to order.
Also, and I could be wrong about this, but I don't think giving gifts to other civs currently does anything. That's sort of something meant for future versions, unless there's something that's changed in this new version that I'm not aware of.