Is this an EFI?  Supposedly if your idle is set too high, hitting the brake will tell the computer to cut fuel because you are braking.  Not sure about the cold start problem.  Do you hear the fuel pump run when you turn the key to ON?  There is a relay that I believe primes the fuel and it has something to do with measuring air sucked in thru the intake before it will turn on the fuel pump.  Check 4crawler's page for some more info on that, but it helped my 88.