I want to ideally keep the tenant and raise the rent to market.

Ive sold off some of my poor performing properties, and a few of my ones that have appreciated considerably so that I could raise capital to trade up into the apartment building arena.

The best of both worlds is hard to have, I always suggest using other funding when you can, however when it comes to getting a deal or not sometimes you have to put your own cash up then get it back out later.

I could do some updates during that time and raise the rent.    

Of course the best course of action is pay off all debts, make sure that you have a emergency fund (usually 3-6 months of salary).  

If you use hard money like I often do (even though I have lots of capital in 3 hedge funds), the cost of construction delays is incredible.

Commingling funds and improper signing are low lying fruit.

Much like those above, I work the 9-5 job and do side hustles to fund my investments.

I would definitely submit a complete offer package with dates, terms, numbers, copy of an earnest money check, proof of funds, or pre approval.

Sure, they could/should have explained to you all the points that Chris raised above from the get go, so that your happiness barometer would not have gone up or down until CLOSING, but - now you know!