At least not until April and possibly May collection are known.

Send the balance due to a collections agency and have them report the balance owed to the credit reporting agencies. 

Look at it again in May and hopefully collect rent in the meanwhile.

I definitely feel bad for our society collectively, but I also don't think they should stigmitize us as landlords--who are really job creating entrepreneurs and small business owners.Us landlords are probably going to be the last ones that government and society will think to need help or assistance.

My questions is if collecting unemployment would effect me refinancing on one property and/or obtaining a mortgage on another?

During the potential 360-day forbearance period, no fees, penalties, or interest beyond the amounts scheduled or calculated as if the borrower made timely contractual payments shall accrue on the borrower’s account.Reciprocally, servicers may not collect any such fees, penalties, or interest during this forbearance period.

It sounds like now may not be the optimal time for you to purchase, but I would keep an eye on the market, on the unit types you're interested in in the meantime and prepare yourself over the next year or so to be able to jump on a deal that makes sense. 

I calculate about an 800 dollar mortgage while collecting 1400 rent.

We are not talking about taxes about acquisition or disposition we are talking about taxes incurred on property that is held and it currently is not held for collection of income as it has not been placed in service. 

I used to collect rent from my tenants and I wasted so much time and just overall annoyance by trying to track it down.