My glue traps are not work (rats flip them over).Is the basic battle plan to put down poison, put down expensive homedepot traps, and seal entry holes?  

You have a vinyl window there and that will be fine in the shower. i would remove the wood trim and tile right up to and about 1/2- 3/4" onto the window. seal the tile to the window with an outdoor extremely flexible caulk used for siding ( OSI brand is good and can be found at home cheapo ), this way as the vinyl expands and contracts it will not crack the seal.

It probably cost me $3K before it was done and I used 3 coats of Kilz on a hardwood floor to seal the smell. 

I decided not to purchase this property, instead bought a house that already has rough hardwood floors (sand, stain, and seal) I do have tiles in two of my other rental homes though, one is marble and looks outdated.

If you are not doing much and there are patches that are missing there is screening and then you can skimcoat the area to seal it.

An exterior drain tile system also has benefits, in that you now have access to the exterior basement wall, which you can then seal and install the proper membrane and fill with gravel for excellent drainage but is mu h more expensive as it requires more work and many times harder to access.The price seems a little high but it might just be your area compared to mine.

Get that building sealed up!

The roof is compromized and was wondering what your thoughts were on replacement roof.Should I just pay the less than $1k to have it re-sealed or should I get an estimate on a TPO roof?  

This would be a legal issue, I would suggest the quit claim if executed, would be in front of an attorney of your choice, notarized, sealed, and copy of the file kept on his file depository, your local UPS Notary will not retain a copy of the wuit claim.

I didn't think of taking pics with smart phones, that sounds like a great option.Slipping it under the door isn't really an option- the doors are sealed pretty well and they are also common entry doors.