So it will require installing some wire from the load center (breaker box).If it's gas, then you just need a 120v circuit but will need gas piped to the location.The outlet for the washer needs to be GFCI.As the previous poster mentioned, the drain line could get a bit challenging as you'll need a 2" drain pipe plus venting for that pipe.

I rent a house (I live in the house), and when it rains alot, and the ground is saturated, a small river starts coming out from the foundation, runs down the cement stairs and goes down a drain. 

I maintain the roof and the black water drain. 

A tenant in my basement unit apt clogged the drain line (per plumber report) and water entered their unit in 2 rooms.

Also are you tying in to existing Storm Drain and sanitary sewer or are you putting in septic tanks and leach fields? 

The basement is all concrete; just an exterior access; it sounds like it was built to flood every so often; the floor drain drains back to the river.

There are ways to deal with this, like drains and window covers, but in my experience window wells are nothing but trouble.

You are thinking this is a problem with a leak with freshwater but this time of year basements often flood because of spring rains/snow melting etc....so could be coming in the from walls, up from the drain tile, not likely to be coming from the sewer if it isn't sewer water but that can't be ruled out either. 

I was planning to make up most of the mortgage payment with the money from the short term rental and now feel like I should maybe try and re-sell it, so that I get out quickly, but that is clearly a lot of money down the drain already.

This allows you some cushion to have a couple of appliance repairs or clogged drains and build reserves to paint on tenant turnover.