Why does my exhaust smell stinky?

Hello,

If you are smelling gasoline odor in the exhaust, it indicated that the unburnt gas vapor passing thru the engine.
It can be due to misfire, too rich fuel mixture.
It can also be due to leaking exhaust valve.

Since you have a rough idle it is a good change you have spark plugs that is misfiring.
When a misfire happens it usually triggers the check engine light.
Is the check engine light illuminated?

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

https://youtu.be/vMwTzURWXmk

Check the spark plugs for wear and gap. Spark plugs should be gapped to 0.060 inch.
If you have excessive carbon build up on the plugs they can misfire. Also if the plugs has not been changed in a while it is a good idea to change them.

https://www.2carpros.com/articles/how-to-change-spark-plugs

I have attached diagrams for your reference.

Please let me know of any questions.

Thank you.