I want to travel to Jamaica but am a convicted felon on parole still. Can I travel or do I have to wait?

You should wait. I seriously doubt if the parole people will give you permission to travel out of the states. If they did (by a miracle) you would need written permission to leave the states. You may be able to get a passport, but you won't really be able to properly use it. You would definitely be stopped on the way back into the country though.

Ok, first anyone can get a passport unless you have been denied it by courts, government or other reason. But a felon can get one of course it is merely a national ID, getting the visa to enter the other nation was an issue.

The real issue will be getting your PO to OK your trip

My fiancé and I are planning our wedding for the weekend after he gets off parole. Would he be able to get a passport before he is released from parole so we can go on our Honeymoon. We would be traveling the week after he gets released.