Where are you in your due diligence period where you can still get out and get your deposit back?

However, on larger buildings one might order an engineering property condition assessment (PCA) from the get go.For this reason, you need a diligence period which corresponds to the size of property - or the ability to extend your diligence period when a deeper investigation is warranted.  

Period.

A buyers broker does represent me but have to sign a contract for a certain period of time and can only go through them.

There is no statutory holding period that qualifies a property for 1031 treatment. 

There are a lot of holes here.You typically can not evict for late rent if the PM accepts the appropriate rent and late fees.A PM should not give 1.5 months notice to move out AND file eviction...it should be one or the other.It's common for leases to automatically renew month to month after the initial lease period. 

HELOC's are a great way to go if you need a good chunk of money for a short period of time. 

Make sure you have a forwarding address for the tenant so you can mail your determination and refund (if appropriate) within the allotted time period.

If I acquire a second house subsequently, rehab it, rent it out (past the "seasoning" period), and try to refi it to get some money out to repeat the process, will I run into issues with the mortgage on my first home when the lenders see that I do not have income from a job to pay for the first mortgage, thus will refuse refinance of the 2nd house?

If you do build up equity over a short period of time, I would rate and term refinance into a conventional loan, and then move and use the VA loan again.