I guess we should have asked what carb you have. I'm guessing you don't even have a regulator for it. That would explain alot. Get yourself one of those pressure testing guages and a regulator. If you call weber north america, they will tell you exactly which pressure regulator to get, or maybe someone here knows the best one as far as reliability and price. I think I had mine set just below 3 psi. per Jose at weber. Hopefully you won't have any other adjustments. Weber could help you with that too. The electric choke sometimes needs to be rotated one way or another. Again, consult with weber so you don't mess things up too bad. This is assuming all your fuel pump and electrical issues if any are corrected.
I ran a weber without a regulator, and it would run until warm, and then flood out to where I had to ride the gas at lights to keep it running. It sure sounds like you have a similar problem.
-I sure hope this helps.
-Adam