Would you still recommend doing the llc as an s Corp if the expected profit was lower?

The rule of thumb is it lowers it 15 degrees from what outside is when it is low humidity...so even if it is 100 with no hum that is still only 85 degrees...best be getting A/C.

I'd like to give them a lot of the equity so that they're incentivized to keep the property up in exchange for financial help with the downpayment and for a lower management fee.

We're talking anywhere from $100k-350k although most likely toward the lower end to start. 

Can anyone recommend where to get carpet for a lower end flip in Louisville, KY.

As far as smaller scale investments, towns like Lyndhurst and Garfield with older homes in closer proximity to one another are still available to flip.Hudson county has a lot of smaller flips or two-three family new construction going on because a lot of the areas in Hudson haven't been renovated in 50+ years so there's a lot more to purchase at a lower price, plus with areas of Jersey City and Union City so close to hoboken and downtown JC and increasing in pricing so quickly, it's a more solid investment.

Surely with the market demand and the fact that his pricing is so much lower he'd be booked up for months on end.

depends on the time frame they give you to close.There are  programs that do not require an appraisal and can close in as little as 7 days from full submission. 

If she did provide you with the claim on security deposit within the timeframe then you still have on option to fight her claim if she should take you to court.  

I understand the mortgage rates are lower for second home compared to investment property.If I decide to rent this property in the future for any reasons (airbnb or leased), is that illegal?