Welcome to the club, it's good to see more LS owners joining. :D
As for your questions, I think leadfoot's covered most of them. The problems you have are the main LS faults and there will be loads of help in he US forums. It's always best to check there as there's loads more LS models there (It was packaged for the yanks after all)
Before you replace the PS pump make sure it isn't just a seal (a common problem) as these are a couple of quid and can be fixed as long as you're handy with spanners, which it sounds like you are.Don't just ignore it though as they can leak onto the alternator on Series 1's and ruin that as well.
My aerial also stays up, the climate control displays are OK, except first thing in the morning( there's a guy who fixes them on ebay who's highly recommended on here) and the wheels are shabby (i've been told about £30 a wheel by a few different places) As leadfoot said the thud is normal on an auto (within reason) and i've just checked my keyhole illumination, which doesn't work either.
Most S1 and S2 LS400 owners have/ have had these problems so it looks like you've got a good deal to me.
I expect you had the same question as most LS newbie's when you were gliding 250 miles back home- "Why didn't it cost more?"
It's because people are scared of the fuel bills/ things going wrong.
(I get about 25 MPG average and up to 30 on a run.)