The IRS will agree to go with whatever the divorce decree states. 

Leverage Your InvestmentsA 1031 exchange lets you use the funds that would have gone to the IRS as part of your down payment on a new property.

So I am assuming he makes money from wood cutting  but claims no income to the IRS and FTB?

A non-resident alien for tax purposes is a person who is not a U.S. citizen and who does not meet either the “green card” or the “substantial presence” test as described in IRS Publication 519, U.S.

You need to contact the IRS to ask for a Federal Employer Identification Number or FEIN.  

That doesn't really matchup with what the IRS says regarding commission rebates.Even if I have the commission on a 1099....if I rebated that commission to a client I know I can deduct that rebate as an expense.

AFR is issued by IRS.

Make sure to keep records of your efforts to market the property for rental to demonstrate this to the IRS.

But the IRS has stated that it is not appropriate in a 1031 exchange where the is the intent to avoid taxes. 

In terms of debts, I agree with @JoeHammel - A title company is the best resource to check on all liens which could be contractor, IRS, bankruptcy, local utility bills or property tax, child support, etc.