Buying a vehicle in Mongolia

Ben,

You need a Mongolian driver license to drive a car in Mongolia.
My Australian driver license was not recognised so I applied for a Mongolian driver license. It's easy to apply if you know someone who knows what to do. My work college did all the work for me. Mongolian driver license last up to 10 years. I do not think you have the driving skill to drive a car in UB because I was so scare to drive in UB, I only drive in the Gobi desert.
I don't have the answers for other questions you asked for.

To get a license it is possible, and getting to cope with Mongolian drivers takes some time to get used to. The insurance is same in every country, you need it to drive without getting tickets and such.

Good luck to you man, you will need it if you want to drive in this country.

Ben,

I was told as of about two weeks ago (when I was at the Traffic Police building to renew my Mongolian Driver's License) that currently International Driver's Licenses are NOT valid in Mongolia.  Only Mongolian Driver's Licenses are valid.  Furthermore, what I was told (by the Traffic Police office/subsection that handles licenses for foreigners) was that they are only issuing said licenses to foreigners with permanent or long-term residency, and the licenses are only good for a year at a time (at least for the first 2 or 3 years, after that you renew for 2 years at a time).  It wasn't that way when I got my first Mongolian Driver's License almost 5 years ago when I hadn't established residency yet, but this is apparently a new thing.  So depending on your status you may be out of luck.

Buying a car is no problem, really.  Though the recent proliferation of right-hand driver-side cars (mostly used imports from Japan) might make finding a low-priced left-hand driver-side car a little more challenging.  I've driven my family's right-hand-driver-side car a few times, and while I can do it, I really would hate to drive it all the time.  It makes passing other cars difficult and dangerous.  Also, the climate and roads do tend to beat the heck out of cars here, so buyer beware when buying used.  And yes, legally you do need insurance.  It's not expensive though (somewhere under $100USD for a year if I recall).

All that being said, though, unless you live outside the city or do work that involves driving, you're usually better off with the buses or taxis.  As others here have said, the driving habits of the locals are pretty intense for most Westerners, and driving in UB city requires a high level of nerve and audacity ("chutzpah", perhaps?) that is far beyond what is normal elsewhere.  Some people can adapt to it, but many either can't or won't (I sometimes joke my many misspent hours playing the 'Grand Theft Auto' series of games prepared me for driving in UB).  I personally see relatively few foreigners driving here, and get the sense that I'm an oddity as a foreigner driving here.  But even more than the drivers, for me the traffic jams are the biggest reason not to drive.  I have a license and an available car, yet most of my driving is just for trips outside the city.  My in-town driving is usually limited to occasional big grocery shopping trips, because the constant traffic congestion doesn't make it worth it otherwise.  I take the bus more often than anything else... it's only 500 tugriks, I don't have to deal with finding a parking spot, and it often takes the same amount of time or even less to get where I'm going. 

Hope that helps.