I have set aside some emergency funds for what will go wrong after I purchase the deal, but I wonder how much is a good number?

There might be some type of "emergency assistance" because the kids are most likely going to have to go to a relative (you didn't indicate if the dad is involved or not).

Here is a tool from Dave Ramsey to help:http://www.daveramsey.com/mobile/gzbudget/Start paying off your debt and start saving.Build up an emergency fund for yourself (6 to 8months livings expenses)Then build up a fund for RE cash reserves.

I live in NYC but invest in emerging markets for cash flow and lower barrier to entry.

Most often I've seen that they hire a property manager and don't fix things unless they are an emergency.

I turn my cell phone off at night ;) We've shown the tenants in our SFRs how to turn off the water if anything like that happens, not that they'd remember to do it in an emergency.

Your area is a top emerging market.Check out the Start Here page http://www.biggerpockets.com/starthereCheck out BiggerPockets Ultimate Beginner's Guide - A fantastic free book that walks through many of the key topics of real estate investing.Check out the free BiggerPockets Podcast - A weekly podcast with interviews and a ton of great advice.

There are some great emerging markets in your area.Check out the Start Here page http://www.biggerpockets.com/starthereCheck out BiggerPockets Ultimate Beginner's Guide - A fantastic free book that walks through many of the key topics of real estate investing.Check out the free BiggerPockets Podcast - A weekly podcast with interviews and a ton of great advice.

Emergency calls at 2am...

If this is all the money you have in the world, then I would set it aside and use it as an emergency fund.