I live paycheck to paycheck and even coming up with a $20 earnest money deposit could potentially be difficult!

He stated that we could keep his security deposit because he broke the lease.

And I usually make a cash offer, with proof of funds, no contingencies, and a large e-m deposit.  

If you do not know what those even are it will be pretty easy to make a mess of things.Frankly you are headed in that direction, note trades do not generally have earnest money deposits.

If I was buying an REO I would give a large deposit 10%~ so my offer looks strong. 

You need to tie up a property with a purchase contract and an Earnest Money Deposit (EMD) and find an investor to put up the money for the deal. 

(I ask this because my current tenants pay me by only TWO methods that are SAFE for me--electronically/online or direct deposit in a special bank account)--are appliances tenants or owner's?

I normally charge two months deposit for tenants with bad credits, but they told me they can't fork up so much money at this time.  

Like @Joe Fairless I use rentlinx, and I also use postlets.comI get a lot of referrals from existing tenants also.I'm pretty specific in the ads about application fees, deposits and background checks.

@Matthew Do you have to put the initial funds up for the construction companies or do you they take some sort of a deposit?