Buy your own infrared camera to inspect the internal moisture levels? 

Typically when there is a perfect line cut around the drywall it is a sign of some type of moisture issues.   

I would think laminate would be your best option, last longer than carpet and less maintenance.  1) Depending on the laminate you use you will need a moisture barrier, the people at home depot should be able to help you.  2) Yes any decent contractor/handyman should be able to knock it out in a week if thats all they have to do there.3) Not familiar with your area but you could expect to pay anywhere from $1.50-$3.00 per sg/ft.  

I couldn't really figure out why, maybe covering some past moisture. 

Rental grade cosmetic rehab- paint, carpet to go, hardwood underneath so polishing ,  install window/central AC and/or fencing depends on the rehab budget. roof, windows appears new. furnace, hot water heater in good condition, no fencing or central AC, basement and foundation in good condition (little moisture there though) waiting on contractor rehab estimate.Rent range - $695-750 . $750 if install central AC and fencing.

The hardiboard planks are too hard to keep up due to moisture and sealing issues.

It appears as if the crumbling and softness is from moisture, and it appears as if the previous owner realized this by installing new water troughs on the roof. 

I'm looking at an off market house in Marysville an I need input from someone who has paid a company such as Clean Crawls to clean, disinfect, replace moisture barrier and insulation.I'm trying to figure out a ball park cost, but none of the companies I called will give any kind of ball park pricing over the phone.  

Wondering if sealing gaps with great stuff and putting an underlayment which is also a moisture barrier would do?  

As far as the basement musty smell, I would recommend adding a moisture absorbing product down there to help eliminate the excess humidity.