you could check if your cat is plugged but the tool is around 60 bucks at matco what i would suggest is to get the cat replaced and see what happens.

or maybe, if your cat is oem, just unbolt it and let it run. it will be lound but you will get the answer on your muffler question.

the other guy is also right about the distributor, if you have carbon build-up or water deposit inside the distributor, it will ark to other contacts and actually firing up the wrong cylinder which we know could be in any position.

do you have a check engine light? just curious if you got a cam position sensor code.

your idle problem could be just as simple as a dirty throttle plate. clean that too.