First off, if they can justify removing the carpet and replacing it, they would need to bill you a prorated amount based on age.

Most people pay off the tax commissioner to have the liens removed.  

REMOVE ALL DEBRIS C OF O REQ'D, SEPARATE PERMITS REQ'D FOR M/E/P.

Now if they do have some use of the space e.g. garage or yard that you're removing from their enjoyment, then you're at a disadvantage. 

I am trying to understand if they would be any challenges with purchasing a lot that has quite a few oak trees as they can't be removed as there are policies around tree removals. could i build a small office commercial unit of about 5000 sq.ft in this lot?

Where the floor is cut to accommodate a stairway, the removed structure must be supported by a header and in a basement that header is usually supported by a post near the bottom of the stairway.

If the law applies and they have not vacated the unit on the day they provided,  get the sheriff to remove them (squatters no longer are required to be evicted).  

I was recently notified by my tenants that they have bedbugs in their unit and they've obtained 3 bids from exterminators for removal.

Hopefully your sale concluded with no hiccups a long time ago.Still, I didn't see anyone really address the questions and since I'm here, I'm the broker for a "flat fee" brokerage, and I have a few minutes so I thought I'd clear the air (responding to your post will shake some cobwebs loose and help me generate some new content for our website too, so there's that).

New Jersey as another example has very loose usury laws and several states usury laws are very vague leaving some to interpretation which can also get you in trouble.