99 Grand Am: Rough Idle and Misfire

I have a 99 grand am SE and its been in the shop so many times I cant count. It was misfiring and they replaced a fuel injector but its still misfiring. It misfires when I leave the car for an hour and start it up. It misfires for 15-20 secs and then quits and runs ok. I have no idea what could make it do this? Leak in an oil pump? Idk?

there is also a vaccum leak I think. Its the line connected to the pcv valve. If you follow the tubing from the pcv valve to where it connects to the throttle body, it has a run off emission tube that runs towards the back of the engine but it isnt connected to anything. I dont know if its supposed to be left like this or if it is supposed to connect to another line?
It definately has a vaccum suction when the car is started.

Can anyone please help me? Thanks : )