They have "sniffers" that can detect very small leaks.Mix dish soap and water in a spray bottle.

Larger holes, I’ve used a can of spray foam then cement over that.

i would put a belt sander in that and fix it in 10 minutes , then I’d do a light matching stain till it was close and spray some polyurethane on it .

Get a quote from a pest control company that you get a yearly spraying contract with. 

Do all your demo work first and at the same time get on the phone and start booking your subcontractors (windows, doors, siding, roofing, electrical, HVAC, plumbing, etc.)...they will likely (if they are good) have a long lead time so you can do any small tasks in between their availability...don't remove your old flooring until you've painted that way you don't have to cover up the floors...just spray and drip at will.

If they spray under the house be prepared to have a hard time with your tenants. 

Then two weeks later I have pest control go back in and bait in the kitchen (or any place else the resident has seen roaches) Also after the spray we put down sticky traps to monitor the activity.  

Is it possibe for me to take them down, spray paint them back white, and put them up again?

What we went with is spray foaming the ceiling joists of the first floor throughout the house then, installed resilient channel in the living room for extra sound absorption.

I use canine, feline, animal, 4 legged furry things that scratch, spray, bark and soil.