Cash Purchases and then financing afterwards

I have been speaking to some real estate broker in central / upstate NY who is saying that a lot of single family homes get bought with cash because banks don't want to loan houses with low prices such $30-60K.  I am entertaining making some cash purchases and then refinancing cash out leaving 20-25% in the properties.

• What I was hoping to learn more about would be people's experiences with making cash purchases for several properties.  Specifically, how the experience of lumping together the properties under one loan has worked for others?
• Also, I was wondering if anyone knows if you can make cash purchases under an LLC for say 3-4 properties and then obtain the financing on those properties once you start renting them out under and have it be under an LLC?

Any help or guidance would be greatly appreciated!