Just want to make sure I’m covering myself before starting on a different system. 

The oil burst up onto the walls and ceiling leaving a residue covering a large area.

After that, the only bugs I'd periodically see were dead bugs covered in white. 

You can always try and cover it with the flooring and/or slope some new mud depending on how much of an area you need leveled.

All utilities are covered by the current landlord, but I don't want to deal with that headache. 

This works fine for smooth transactions, but won't cover you if anything goes wrong.

I have a lease template that covers my states legal requirements.

I also took his list to Lowe’s and Home Depot and created a price listing covering each item.  

Also - I’d look into the history of the condo fees - do they raise the fees periodically and what do these fees cover?

If the landlord is named on the policy, then the landlord is also notified if you cancel the policy (which would put you in violation of your lease).I would talk to an insurer about the amount of the policy - renter's insurance can also cover damages caused by the renter (you) and as well as the contents of the rental unit.