The lathe is not securely fastened to the structure, potential moisture  problems, foundation movement, etc.  

Does that really take care of the mold that attached to the flooring (due to the moisture issue after the mold crept up all the walls it flung itself onto every single thing in that house lol including the floors), or is it like mold on bread where the mold has roots and is all over inside even when the surface is sanded off?

Be gentle with any stupid questions I may have

We didn't smell mold, and the only moisture was coming from a small leak in the water heater. 

AC is barely working,There were some moisture issues underneath the tub from the upstairs bathroom. 

Use a moisture meter $20 at HDepot to check it.

Get your wood moisture below 12% (some contractors use 15%) before any rebuilding. 

I have one rental in Louisiana and when we got flooded... the rental lease is not in effect anymore as the house is not live able.... it's a pain if u don't have insurance.... if ur renters are good for it.... at least ask them to take out their stuff in the curb... a lot of renters just here just left.... and landlords has to do all the hauling away of their thrash too...On the gentle note.... pls be cautious when talking with renters... pls be kind and understandable that they too lost a lot of their possessions aside from the fact that they might not have a house to rent as housing demand will be very high....

We're ordering a mold and moisture test, if they come back good (pass) should we be concerned?

Moisture Management Plan, certified by the Servicer 11.