are there more than 2 posts over this issue??? you have 2 codes that will cause the engine to not run properly and yet you ignore them seemingly knowing they have nothing to do with your issue.
go get the error codes taken care of, the gas cap is easy and cheap, just go buy a new one put it on and see if the dash error light associated with that goes away, it'll possibly clear the other evap code as well (it's also possible you've damaged your Evap canister)
And since both of those do have an affect on the running condition, it will cause you idle/running problems.
lots of good advice over it but as mentioned already, you do the opposite..is it possible to have Jeep Munchausen syndrome ????