I looked into the right of redemption period in NC, and it stands at 10 days after the end of the foreclosure sale.

Sorry to hear so you are dealing with so much in such a short period.  

Real, substantial success versus using say a 10 day inspection period.

You of course get their info to periodically follow up.

There is a period in which the owner can redeem his property after foreclosure .

Or just refinance at the end of the period if you have substantial appreciation built up with equity and use the extra money to purchase more properties.

I'm just about your age too, I started with a Capital One as my first credit card, then opened a Citi Card as well, if they see you paying off your balance in full every month they will gladly increase your limit and you will start getting tons of cards in the mail, don't go too crazy though as applying for too many cards in a short period of time will negatively impact your credit score. 

I would like to make savy investments and over a long period of time eventually generate enough income to live off my investments (make at least 50-60k a year) with 300k capital and no current income. 

Although, the sale was for $550,000, only $110,000 was received the first year, the rest is amortized over a 30 year period, and is received in payments that includes interest and principal.

Make a reasonable assumption about the rehab required, write a contract with a reasonable inspection period and make an offer.