Your primary residence would not qualify for 1031 Exchange treatment. 

Hiring of this PM occurred because when the tenant became a problem I had just brought my sister, with terminal cancer, to my home to care for her.  

hence why its vital to have a record/receipt of any rental property having been treated (ie, sprayed or 'heat' treated) in between each tenant.absent proof of  a preventative treatment before tenant moved in, its up in the air if they are blaming landlord for an allegedly pre-existing condition.i'd give them the option to vacate if they can't take care of the pest problem as its a single family detached.

On a side note, I have seen in court in a very landlord friendly state, a landlord slammed with 4 figure fines due to illegal treatment of tenants.If you don't want an attorney, get the NOLA Landlord-Tenant book for your state and learn it backwards and forwards.

I am trying to evict him because I don't want bad thing happen like fall from stairs or even he die at property (because he got cancer)My questions are:Is the eviction right thing to do?

Included in that service is free emergency treatment if there was ever an incident, like an ant invasion.The monthly fee isn't that bad. 

It's possible the tenant checked in to a treatment facility in FL. 

Section 8 tenants are not aliens or people seeking lesser treatment, lol.

Here's a version from Wikipedia:There is a considerable body of case law concerning the proper treatment of a scrivener's error.

The entire crawl had to be treated total cost was 2500 for a cleaning treatment, remove old vapor barriers, and install new.