After I take possession of the property, I want,to install a new LOCKING MAILBOX for my unit. 

IF by some miracle they accept the cash and actually do relinquish possession, you get in there as soon as possible with a reliable GC who's willing to renovate the place in January.Then you put it on the market, reaching out to just as many agents as you possibly can.

When I took possession of the property I atomatically raised rents 20%.

If they are, you can just serve a 30 day notice after you close and take possession of the unit that way.

http://findhoalaw.com/code-of-civil-procedure-section-325-adverse-possession/Your mother is not required to do anything.  

When the closing entity simply holds your money in their escrow account after closing you are deemed to have constructive receipt (meaning control if not possession) of the money. 

Make sure you possess that skillset

That is, you can’t use more than 10% of your net worth exclusive of your home and possessions, per loan.

The tax deed purchaser is not allowed any possession of the property during the 6 month period. 

Most leases you sign have a clause in them protecting the landlord in a situation where the landlord is unable to deliver to you possession of the property.