I suppose it depends on the 'Dealer' - if it was a Lexus agent, I would have thought they should have checked the A/C before putting it up for sale. If its a trader, then who knows what sort of response you'll get from them or what sort of cheap bodge they might do to sort these problems in which case you might be better off sorting them yourself or by someone you can trust.
If the A/C compressor is kicking in, then it must have at least some gas in it. I have a local guy who will drain the system, pressure test, then refill with the correct volume of refrigerant and weight of oil and a dye (for future leak diagnosis) for about 70 quid + VAT. I'm sure there are many other similarly competitive places around near you.
The wheel wobble is an odd one which I used to get but seems to have disappeared now. I've heard everything form wheel balance, buckled wheels, warped disks, sticking brake pistons and upper wishbones to be the cause, so let me know when you find out which one is causing yours! :o