New Investor - Rental Prop. budget question

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Hi, I have read all the books, and feel very educated, but now I need to see real estate investment in action. This forum has already helped me, and I've looked at it for about an hour! I stumbled across someone mentioning a Real Estate Investment Club, and I found a local one to join!

I do have a questions though, all the books talk about, "no money down," and using other people's money. I know how to get 100% financing, and even how to roll the closing costs into the loan, but my question is after closing.

What happens if a major problem occurs in the rental property, bad roof, flooded basement, or some other major cost disaster? Should I budget money aside just incase of these things, is there an insurance out there for landlords that cover these things? Also, during a rehab do you need to carry a full insurance policy on the property while it's being rehabbed? Thanks for the help, Chris