This will be my 3rd season in my 2010 Camaro. I am an advanced driver through NASA, and we are almost done prepping my car for One Lap of America
Brakes - I've had the best results with Carbotech xp10 (front) and xp8 (rear) pads. I use cheap, takeoff OEM rotors and throw them away when I replace pads. I bought some stainless lines and use Superblue fluid.
Wheels and Tires -I ran 275's on all 4 wheels with factory 9" wheels for two seasons. I have since upgraded to 19" Forgelines and 305/30/19 tires.
Suspension - I bought the Hotchkis race pack. It's streetable and Hotchkis wins a lot of events. If money is tight, replace the rear sway bar first and lower the car. That's likely where the most bang for the buck is.
Engine - I ran two seasons with headers/air intake/tune which really wakes up the car. I recently went with a cam/head package but have not track-tested it yet. Even 100% stock I still had a good time with the car.
In answer to your questions:
1. The car works great on the track. Chevy did a great job with the indpendant rear and the brakes are strong.
2. I haven't had any heat issues. I have run the car on the long course at Pocono on a 95 degree day and it didn't do anything odd. You may have issues with your automatic transmission. Change the rear differential fluid frequently - Chevy recommends it and I think the friction modifier they want you to use has heat issues.
3. The automatic may be an issue because it's going to get hot. I would buy the biggest cooler I could find and learn how to pump out all the fluid after each event. I have seen a few C5, C6 corvettes with autos and the occasional mustang. They all have become experts at heat management, so assume the auto is "less than ideal".
4) I don't think your Corvette wheels will fit.
5) Other issues? Nothing terrible. The power steering resevoir tends to suck air on hard right turns and you can feel a little shudder. I changed to a different fluid and it got a little better. Visibility out the front window isn't the best, and the car has fairly large blind spots. 20" tires aren't ideal, but you can switch to a different wheel size for the track. If you do the square setup with OEM wheels, Nitto has the NT05 tires in 275/40/20 which is pretty good. There is also a Toyo in 285 that is popular, but I have not tried it.
Stuff that broke:
Two side rocker panel moldings. I went off the track and ripped them apart. I got painted takeoffs on ebay, they install in 20 minutes. I was lucky this was the extent of the damage.
Clutch release bearing. Mine exploded. I drove a couple more sessions at Lime Rock Park in 3rd gear and just didn't shift much.
By the time I got the car home (trailered) the clutch and slave cylinder was ruined as well. I replaced with OEM units because I was heading to Watkins Glen the next weekend and that was all I could get on short notice. If I need to do another clutch, I would probably get the ZR1 double clutch or aftermarket equivalent.
The left rear hub bearing got noisy. I replaced with OEM (warranty).
I have replaced the outer rubber boot on each axle shaft twice. This is a known issue with lowered cars. I am looking for a better quality boot now.
The black plastic fascia that covers the mufflers melted. Known issue with heat, cheap and fast to replace. You can cut 1/2" off the rear pipe and slide the mufflers forward which makes them melt more slowly.
If you have other questions, I'd be happy to share what I know. Feel free to email or PM me here.