I have a gas stove/oven and am wondering the on the do’s and don’ts of self cleaning. First off I have a broiling pan that came with the stove, it’s the same material as the inside of the stove and is a pain in the ass to clean, can I keep that in the stove while the self cleaning happens? It isn’t all that dirty but I want to do the self clean anyway, so how long will I need to set the timer for? And can I leave the home while it self cleans to avoid having to deal with the burnt smell? Oh! The stove top burners, super dirty as well, can I put them in the oven to burn off the residue!? (This was a foreclosed home) :(

Nothing should be left in the oven. The clean time for the oven is based on how dirty it is. Look for a website for the brand of your oven. You might find useful tips there even if it is an older model.
Try soaking the the other things in hot soapy water and get some Barkeeper’s Friend, which you can find where you would find Ajax or Comet typically. It cleans almost everything, although you will need a bit of elbow-grease too!