It is common practice to use sealant on exposed nails in roofing to prevent water penetration.

(I have seen that mentioned a few times)  I have had it tested with the isolation and camera and there are at minimum 6-7 leaks half of them root penetration from very large trees surrounding the foundation.  

I would just make sure there isn't going to be movement, water penetration, or bug penetration.

I had a roof leak that took a while to find because it was coming from a plumbing stack roof penetration much higher on the roof. 

I'd consider LED as they can take more abuse (on off on off on off) (moisture), and they're cheaper than a new fixture....  

But for a basement, tile is really your best choice due to potential moisture issues (esp in your climate) That said, I  googled some photos of the stuff.

Category 1: the basement shows some hairline cracks at the frost line; and some stair step cracks but no heaving, and only minor evidence of moisture..Question: what type of repairs should I plan for?

Interesting...it almost looks to be sagging, but that is usually caused by moisture or a structural issue...but there is no apparent water damage...It could be faulty material or the contractor didn't use the correct installation process...the other consideration would be climate...expansion and contraction that causes the drywall/mud to crack over time...IF it is sagging, there needs to be some more investigation...the contractor will drop the ceiling back to the next rafter and poke around to find the cause...that is an open-ended repair...you can get a cost for the investigation, but no the repair.A final thought would be that if it's just cracking and there is no sag, install crown molding... 

She stated the first year she has a renter she schedules quarterly visits to change out filters, and check under sinks for leaks or moisture problems, and check smoke detectors, ect..  

I mean, mold all over the walls with moisture damage, and it appears that the tenants are hoarders.