Then add on holding costs and loss of lease for the 9+ month construction period. 

They must have gotten a 3-day notice and she assumed the others remained and were evicted and that she had an eviction filed against her because she was on the lease.

Review their lease agreement and addendums.

I'm assuming the lease stays in place and I don't need to write anything new, or am I mistaken? 

Landlord has been accepting $2k instead of the agreed $4k since 1.5 years and now all of the sudden he is asking us to pay back rent to continue the lease.

If your ratios are close it is possible that a new lease on that property might give you the income needed to qualify. 

In the past, I have adjusted the due date, set up 1099 type tenants on a quarterly payment schedule, requested (and received) 2-3 months rent in advance, sold the property via lease/option, etc.I get that the norm is rent due by the 1st, late fee accrues on the 6th, but this tenant's situation apparently doesn't fall into the normal category, so ask the question, then evaluate whether you can live with (and accommodate) the answer.Good luck!

If a Lease Option in Texas is structured the following way will it be legal? 

The lease had already expired last month, and they have not signed a lease renewal form that I sent them 30 days before lease expiration.

Consider having their parents sign your lease.