In our case, the stains disappear after the counter dries out thoroughly- several days to a week.

Many have no idea of what they are doing, but because they never got thier tails sued off they think thier way is best, you need to be able to spot them before getting involved.Learn RE financing, it's almost as dry as insurance.

Yep, and have them shoot the grade at about 1/4-1/2" a foot if possible so water doesn't run too fast washing out, use larger rock in base and fill cracks with smaller gravel....it's what we do around here....if you're guy doesn't know what he's doing, get someone who does for your terrain and soil type.

One place literally before the ink dried the tenants where already calling about issues.

They are caused by settling soil.

So will gutting the dry wall (ceiling and walls) be enough for a contractor to determine if the framing needs repair?

They have dried up considerably just like everything else and their standards have increased on real estate deals since the bank regulators have tighten up so much.

Buy a couple of dehumidifiers to dry things out.

Perhaps you were attempting a WHOLESALE deal, but regardless, dry run your first purchase with RE agent representation to learn the ropes. 

If you don't have a professional property manager hired, you can probably expect to pay about 10% of your gross rents for vacancy while looking for a new tenant or might need to make repairs from the last tenant)10% of gross rents for water, sewer, trash, and snow removal (even if you're not running on city water, you still should be budgeting money accordingly for water because at some point, the pump in your drilled well is going to give out and you'll be left high and dry unless you have the money to fix it.