If a dog damags your property IE: staining wood floors with urine the tennant is responsible for repairs. 

Otherwise, you can re-stain them with a close enough color to minimize the amount of rework.

Cabinets: is cabinet staining something you'd recommend as a DIY?

Granite is quite effective as it is scratch, stain and chip resistant.

You could always sand and stain them , a couple coats of gloss poly and you would be surprised . 

It makes the towels less absorbent and they hold onto stains much more readily.

The hot mop dude takes pie when pie is passed, the Marmorino plaster artist also books two jobs at one time thus he will hold you up if your schedule is not in stone and you want that smooth marble look not popcorn from the guy with grease stains on his rear. 

Since it's the ceiling, when your plaster man is finished with the repair you can bank on it it's going to need special primer to hide the water stain and a respray of the ceiling color.

The one I am most concerned with is the moisture stain, were they able to figure out where that is coming from? 

@Jason Staine I don't know much about Lead Propeller so can't comment.