He also said that since there's no mold, I don't have to have replace that section that was wet, it can just be primed and painted.

You can cover up the worst pet odors with that stuff and the pets wont come back and use the floor as a bathroom anymore (cant smell their previous escapades), should help with the water 'wet' smell.

Running down causes less warm air condense and makes pushing wet air easier.

I ultimately want to re-hab while I live in it, then within a year or two, sell to get my feet wet in rehabbing or hold onto it for a long term rental.

Hello,      I'm new to BP as well as REI,  I've done lots of homework and feel ready to get my feet wet on my first deal.  

I hate water damage.However, in this case, you may be able to fix the warpage by wetting the area again, and putting something flat and super heavy on that area to warp it back to normal.Unless this is fake laminate?

But if you are just trying to get your feet wet and get started you can invest OOS by buying a rental in a great market OR invest passively in a deal is another option. 

The HOA has started on the repairs and cut out the wet drywall and used blowers to dry the rest.

Also I wanted to buy a motel because I've been wanting to buy a motel for a while, and I figured this was an excellent opportunity to get my feet wet.

They sold it for $100,000 more than they paid for it 4 years ago and still want me to cough up $600 tomorrow?