Hardwood is beautiful but expensive and easy to scratch and is finicky around moisture and humidity. 

Is there a reliable method/way to maintain a constant moisture level year-round so as to protect the foundation from shifting that would compromise all of the extensive renovations that have taken place?

Any moisture trapped will just cause mold.If the cracks are small or hairline cracks you can most likely go over the existing grout with no issues.Where the tub meets the wall there should be no grout EVER.

Low spot is about 1/2" lower than a high spot.We also found that the puddles form in the crawlspace when it rains, and it's very likely the flooring sagging due to structural damage from the moisture.

About $6K to replace the HVAC itself.Give the mold, you might eventually need the air ducts cleaned.Do the bathrooms have vents to get rid of excess moisture during showers/baths?

but to just stick them in there and never check.your going to have filters never changed and maybe ruin your HVAC.. your going to have water leaks that cause dry rot..your probably going to have plumbing issues.. you have a tiny leak in the roof and next thing you know mold behind the walls.you catch them putting sheets in the window or even worse  Aluminum foil which creates moisture and moisture damage and mold.I can go on and on.. this is the benefit of self managing.. and if your not.. then pay your PM to stay on top of these folks. its money well spent.. both for peace of mind and your pocket book long term.My A class new construction that rented at 1400 to 1700 which was the very tippy top of the market..

Doing a mild inspection with pictures- My inspection would consist of identifying appliances, capital expenses, and overall condition such as moisture or structural issues, This will include a lot of pictures approx 100-1505. finding an investor to flip the property to. 

Most 100 year old houses are going to have some level of moisture in the basement, though. 

There was not sufficient ventilation in the laundry room or back bathroom to keep moisture from accumulating (note: there is a window and a door).

all of the houses in 1 sq mile are cookie cutter 1950's brick ranches. that street in particular is no different. lawns are nice, very nice looking on the outside. but when you go inside, 80% are still stick in 1970's.i am trying to post a picture of the windows, to show how bad they looked. these are steel pan windows that had rusted over the years and moisture was killing the window. cold air was leaking and furnace bills were sky high.seems like the picture is huge and have no idea how to resize it.