OK, yes they are very good on track, I've never managed to overheat them ever.
Not sure on the size of the adaptor, just buy the kit from rally design, it'll fit.
Spring rates depend on the setup of your car and personal preference too. I seem to recall someone saying those gaz coilovers come with 275lb springs in the front which are pretty stiff really and I'd probably not want to go stiffer if you use the car on the road a lot. I've got some 375lb ones to put on mine for the next track day (which will probably be next year now to be honest, too much other stuff going on to get my car sorted out for anything this year). I have a subframe and no anti roll bar too which requires stiffer springs to counter.
If you are wanting to go on track I'd seriously consider saving up for a decent differential, it makes such a good difference, I'd buy that before doing much to the engine. If you can't put the power down on track you're not going to be fast no matter how much power you have!