Okay guys I'm new on here and I'm asking for anyone's help on how they might approach this deal.My uncle has a neighbor who is letting her home go to foreclosure.

You could take a couple of approaches... (1) a full (or partial) tenant change out with notices you mention; (2) let them all revert to month to month (or do new month to month leases with your terms is better).

They approached a couple property management companies in the area to get rates, then approached me asking if I would be interested in managing it for them for that rate, instead of them paying someone they don't know.

I'm wondering how flippers approach something like this.  

If you are referring to the ability to terminate the tenancy at your discretion sooner, a M2M tenant would generally be the correct choice, but perhaps the wrong approach.

I found a 6 unit that "supposedly" gross 40K. So I ask for the income and expense statements, not sure what they are called in the real world, and the agent says that owner managed the property himself for the last 10...

I believe the approach you described of using the market cap rate against your increased NOI to determine the increased value of your property is more appropriate for commercial buildings (5 units and up).

I'm not sure if lenders lend on multiply properties being sold in a package deal so I'm not sure on which lenders to approach just yet. 

We are also looking for private lenders. what is the best approach in reaching out to private lenders in the south florida area

I would happily offer my own state's approach on these kinds of issues, but I don't think it would be that helpful to whomever is asking the questions.