David,
If you use better brake pads + get some cooling to the front, I think you'll find the brakes are actually very good.
I'd suggest to stay on street tires - its way easier to learn with them and yes, the sensation of a loose rear end is what makes these cars fun to drive IMHO. Until you can consistently rotate/slide the car in a controlled manner, I think streets are better.
As most suggested, it does look like you can use more rear springs
I am using 33mm and so far so good - though you can never be too stiffed in most cases.
On the engine front - if you are not running crazy boost and oil temp is in check, why the worries?
Have fun and let her rip !!!