P0300 code?

Yep, the random misfire code, these are caused by a vacuum leak most of the time, especially with the rough idle. Here is a video to help you find the leak:

https://www.youtube.com/watch?v=LRKWV4Are5c&t

Also, can I ask if there is an exhaust leak? This can cause the issue as well. Can you upload a short video of the engine idling so I can see? This would help.

There is no exhaust leak and I will try to get you a video

Hope this helps

That was one of the better videos, thank you. I would clean the throttle body, this guide can help. Please check the images below as well.

https://www.2carpros.com/articles/throttle-actuator-service

Also, lets use a scanner to check the LT trim an ST trim to see what the computer is doing. We may have a weak MAP sensor. I would still try the smoke machine for the vacuum leak, sometimes the spray misses the leak. Read the guide completely before you begin. Please upload a video of the throttle body condition :) Check out the images (below). Let us know how it goes