Can she facilitate this transaction under herself or any entity because she’s the sole owner and taxpayer?

That's done here: http://comptroller.texas.gov/taxinfo/franchise/webfile_franchise.html IMPORTANT: To do it online you'll need your taxpayer number (which is public and will be on the forms you've got from the steps above), BUT ALSO YOUR WEBFILE NUMBER.

Most taxpayers choose option one if they also have other investments that produce income such as partnerships.

Your SSN is your tax payer ID number if you operate as a sole proprietor (no entity like LLC).

Commissioner, the taxpayers exchanged one lakeside vacation home for another.

The taxpaying entity that is invested in Real Property has to both sell the relinquished property, then buy the replacement while following all other 1031 exchange rules for the exchange to be deemed viable. 

This will make your yearly tax payment pretty high.

I see a number of starting points:The current owner hasn't been seen for at least 5 years -- the over-grown lot reflects this.He's almost two years behind in his property tax payments, so the county will be taking some action in the near future.  

The taxpayer has to the 1031 exchange.

I would debit tax expense (increase an expense) and credit property tax payable (increase a liability).