If not, it's a gov't insured mortgage for a reason.3.

My advice would be to speak with a good insurance agent and just make sure to purchase the right insurance and enough of it that you're comfortable. 

You may need  the following people on your team: mortgage broker, insurance agent, RE attorney, accountant, GC, handyman (down the road).

I am unsure of how to proceed though because my exterminator says that it has bed bugs.During the renovation, the former tenants’ furniture is being permanently removed and the flooring is going to be changed from carpet to vinyl plank.

Make sure the end game is locked in before proceeding. 

Unless you can afford two mortgages, you need to make a purchase offer subject selling current home and use the proceeds as new home. 

Generally, Realtors rely on title insurance companies to search title history.

To set the stage, here are a few key points:Property:2 story townhouse2 bed / 2.5 bathMostly carpet18 month old (yep, its brand new)Situation:Nobody was hurt to my understandingTenant did not have rental insurance even though it was required in the lease per my property managerTenant admitted, in writing, they caused the fire.Kitchen fire that burned the kitchen completely and I have smoke damage throughout. 

Are there reasons why I should not allow my tenant to proceed with this project?

Perhaps, this is something insurance would cover?