The moment the pre-payment window is done, the investors chances of loss via refinance increase.

When the time for the Refi comes around on a 1-4 unit property, I was under the impression that the appraisal is not based on how much you have increased the rent during your hold but rather just the typical appraised values of other similar properties in the area (whether it be other 1-4 unit properties or single families in the area) and that the increasing of the rents while holding the property only comes into play when the asset is a 5+ unit property - is this correct?

It's unlikely that any actual tax would be due because of the increased $11.18 million lifetime exclusion, but you're supposed to track the exemption used and technically have a filing requirement.

Once she is paid off the cash flow is all yours and your P&I payment wont increase because of a higher loan after the refi.It would be nice to no some of the figures .

By requesting a jury trial, they increase the amount of risk, time and money involved if the parties do not reach a settlement.

This is because it was purchased to be a good home and not necessarily a good rental.If I were to invest OOS:I would not choose the highest cash flow Midwest locals but would look for a location with increasing population and constrained in some way in their RE growth prospects. 

My question is does it make sense to hold a single family in a market that the rentals are low compared to the sell price and focus on the long term value increasing or should I sell and have a clean start in a new state?

We immediately gave 30 days notice that the rent would increase to $300/ month.

You can find duplexes in those areas that need some work for around $150-200k that will already be cashflowing and with some renovations can increase cashflow.I've done this and on my first duplex, I was able to get a $25k line of credit which I used to purchase another duplex. 

That is negative $100 cash flow.To continue to hold, I could refinance to lower mortgage to about $1000, increase rent to $1600, cancel pool service and cash flow about $360.Or terminate lease for a struggling single mom and take the cash to turn into a larger investment.