This can vary by state/jurisdiction, but an eviction (Unlawful Detainer) is typically the process by which a landlord seeks to have a tenant removed from a property that they continue to occupy/use/have possession of in violation of the lease. 

Kinda the worst of both your scenarios, plus one you didn't mention: long term tenant, followed by a long vacancy - one month before we have legal possession and have removed their chattel and 4-6 weeks beyond to refurbish the property ... we'll be lucky to have it rented by Jan.

If you succeed, you will get possession of your unit sooner and less expensively than going through a full-blown eviction.

Keep in mind you will have to provide the labor to move the tenants possessions to the curb

They seem to be much more profitable, dollar for dollar invested, than single family properties and possess a number of advantages from the investor's POV.

No, do not give any time, they need to move out and if don't, get the writ of possession.

These people have possession of the home as their residence, therefore you have to evict.Do so ASAP, then as soon as you know they were served return with your offer now that they know you are serious.

according to the article  the killer was a convicted felon in possession of a firearm

10 years ago I received a misdemeanor for possession of a controlled substance in the state of MS., everything else on my record is expunged, I have passed several corporate background checks etc.

Meanwhile, if you have control of the property and possession, you ought to be able to put a tenant in after some level of renovation and get cash flow while you clear title.