The issue is with the second floor tenant, they've been there for 5 years and never had a rent increase.  

I realize now, that I made a huge mistake buying new and I can greatly increase my monthly cash flow for other, more important investments.

That would increase your savings rate! 

Or, can I just have them sign the new contract which would have a rent increase and pet deposit/fee? 

If he does not want to pay the increased amount he will leave in his own.

If I buy a property built before a certain year that currently has tenants in it, I cannot raise there current rents beyond the allowable increase for the year(3%-4%)  I would have to wait until any of the units becomes vacant to raise rents to current rent rates.Is this correct so far? 

(Credit score over 800)2018-We committed to increasing our real estate holdings.In February we bought a condo in Pensacola, Fl.

Imminent Interest rate increases through 2019 will negate any appreciable price increase and indication of a general cooling off nationwide is coming.You should approach the lenders to let them have the project.

But instead I'm debating on doing only a 20% down, which will be a significant increase to my current mortgage on the smaller house, and use a good chunck of the 20%, to either pay off student loans ($65k, saving about $700/mo in payments that can be used to offset mortgage), or using it to put down on rentals (multifamily). 

However, due to the appreciation play, we can see this increasing 3.5-4% over that time, including maybe 5-7% each of the first 3 years.