I see too many of those mailers where they are trying to trick people into an ARM or with hidden costs. 

And the banker told me if I join Chase private client, they can do a cash-out refin on my current house and extract $290K out of it, so I can pay the investment house all cash, and they can do 3.75 for a 10/1 ARM loan.Should I do it?

This also apparently is a 'commercial loan' , with 20% down, 25 year loan, and ARM with refinancing every 5 years.I've been given data on income/expenses over the last 3 years for this particular unit, along with data from our lender.  

20 year 5/5 ARM 20% down minus repair allowance of $10,500 (applied towards down payment), seller paid $3000 closing costs also.

The lease explicitly states that anything besides toilet paper and waste is the tenant's responsibility.

As licensed contractor types charge an arm and a leg just to paint or do a basic turnover on an apartment

I'm not trying to twist your arm or anything, but high quality properties are not the PM headache that a lot of people cry about.2) Generally, I would say somewhere in a range of 10-20% of your investment capital should be held as a cash reserve. 

The terms of the loan would need to market/arms' length.

I do my local banking with RBC and I've been pre-approved by them for a 7/1 ARM 30 year @ 5.125% . 

My commercial lender I'm using said the early pay off fee is 2% for the first 3 years, for a 5/1 arm.