'Just fine' is a relative term. What may be just fine for me might be horrible for you. Is this car new to you, or if not, how did this problem start? It is usually a good idea to confirm that your engine is timed properly, by doing a compression test, before you start diagnosing elsewhere. Compression test on your car is easy: pull the F1 fuse, pull all spark plugs, well charged battery, and floor the gas pedal when you are cranking. On your car, you should get about 190psi on all cylinders. If you do the compression test, post your results.
Also confirm that your check engine light is on with the key on, and off once the car starts.
You should give details about how the car starts from cold - what the cold idle is, how/if the car warms up properly, what warm idle is, etc.
From what I gather from your post, when you brake, the engine dies - does this mean that you brake, and the car slows down, idle drops until the car stalls? Or you put your foot on the brake, and the car shuts off immediately, like someone turned the key??