Engine will only start and idle rough with the oil cap off

More then likely the PCV valve is clogged so we need to start with replacing this.

Here is a guide that helps with this issue if this is not it but the fact that the oil cap being removed makes a difference makes me pretty confident that this is the issue:

https://www.2carpros.com/articles/stall-at-idle

Below are the instructions that will show where this is and how to replace it.

Let me know what you find after this and we can go from there. Thanks