There are a lot of decent flip deals that I'm salivating over, but I don't have any funds available right now. 

My parents want to get a house closer to town. so my thought was, could I potentially just purchase a multifamily house in Lafayette Indiana using a low down payment financing, since I would plan on being there for a while myself, then rent the other side to them (under market value and less than the crazy high mortgage they pay now, but still high enough to fill an emergency fund into the house) I would be using my own low living expenses to build up capital for my next investment property.

In general you should be able to get > 50% ltv.

I am working on building capital to fund piggyback deals--so I can buy the next one while the current one is closing.

Now the sellers son has decided to stay and squat at the property for another month til the end of september, with the exception all of the escrow security funds coming back to me (buyer), am I entitled to split or give up any of the escrow funds with the sellers son due to him squatting in my new property.

Funding in as fast as 24 hours. 

Lower price points and I'm working on building a track record and resume to have potential investors fund me.

I'm brand new and will only have funds to invest in one property at a time and don't want to get in a situation where I may have accepted offers on multiple properties but I only have enough money to do one. any help the community can lend would be much appreciated.

You can not lend yourself money and not actually fund the loan.  

Usually the lending amount is a percentage based on the LTV (Loan to Value) or LTC (Loan to Cost).