The Mr. was arrested over the weekend on a Domestic Violence and a possession of a controlled substance charge.

I'm not sure about Albany County, but be careful, within nys they're is a statute of limitations where the ow er has x amount of months, years etc to pay the back owed taxes and take full possession of the property.

Because it's legal in CA, he may be well within his rights to have possession of it.

And change the locks as soon as you take possession...

This person is NOT a squatter since your parents granted her access to the property.You need to file 30-day eviction for possession, not 7-day for nonpayment.

Not taking possession, not receiving deposit, and lack of habitability (e.g. you had a fire). 

The house is in general good condition, but apt is rented under market value.The seller refused to give notice to the current renter, they also refuse to request the renter to clear their stuff from the attic, basement and garage, all of them currently being used as additional storage (even though none of this is stipulated in the lease agreement).I would like to give notice to the renter, as soon as I take possession of the house that I will not be renewing their lease.

Obviously, any buyer would discount the price they’d pay, due to not having possession/use of the property for an unknown number of years. 

It was not clear from your note if this is really garbage that has just been put in the wrong place or if this is a bunch of crappy possessions that the tenant left all over the driveway.I'd probably contact the tenant (with a good paper trail) letting them know the city has cited THEM for the violation. 

The tenant allows a violation of MN Stat. 504B.171 Subdivision 1 (allowing controlled substances, prostitution, unlawful use/possession of firearm, stolen property on the premises).The tenant has materially violated the lease, other than nonpayment of rent.