I agree with you that the stock brakes are fine. I've changed the brake fluid to Total high-temp fluid but other than that run pretty much stock including pads. Never had a problem.
- Is it my driving? Should I just slow down more for the corners?
It's important to keep the car balanced so if that means slowing down, yes. You shouldn't be fighting the car; the car talks to you just like a human being but in a different language. It will tell you when it agrees with your inputs. The smoothness of your inputs goes a long way.
Do you have an instructor in the car with you?
- Is it the tire pressure? In another post, someone said they ran cold pressures of 45 front / 42 rear. Should I go higher in general? Should the front be higher than the rear?
Those pressures sound very high to me but I don't autocross. For my HPDE events I run stock tire pressures cold and then about 34/38 hot. I would always start with the pressures listed on your driver's door.
- Is it just the stock 335i? And if it is, then what are the mods that would be the biggest bang for the buck for tight autocross cornering?
Is it just the stock 335i - yes and no. If someone else can get in the car and drive faster than you, then the car's not the issue.
That said the cheapest way to go about changing handling is the tire pressures. Experiment pumping the front up some, that will improve turn-in responsiveness. I would only change one at a time e.g. change the front pressures but leave the back alone. Tire pressures won't make a night-and-day difference but hey, it's a $0 mod.
The next way to improve handling is to get a good alignment. Do you know your alignment specs?
The PS2s were a good choice in tire; they were stock on some BMW M cars for a while. Michelin Pilot Super Sport is the next step up from those, I just personally put those on my car and am blown away by the grip (coming from Hankook V12s). They are just awesome for high performance driving. Many cars at the track this past weekend were running them, some owners on their second and third sets - only praise coming from the owners.
Next after that you could consider new springs and dampers. Forget sway bars, etc - dampers/springs are 80-85% of the suspension equation (in terms of bang-for-the-buck difference). Koni Yellows/Sports & stiffer springs like H&R Sports or Eibach Pros (for a more modest drop) are an economical choice; after that there's AST 4150s/Swift springs - just as examples. The stock 335i dampers are severely underpowered and get overwhelmed by even small turns; they are certainly not helping you in autocross, as heavy as the 335i is. You'll be surprised at just how much of a difference a good damper and spring combo can make.
So in short...
-Driving habits first (do you have an instructor?)
-Tire pressures (small difference but $0)
-Alignment (please post your specs)
-Tires (if your PS2s are still good I'd wait till you wear them out)
-Dampers/springs - by far will make the biggest difference in your car's handling ability