It's best to view Stripe Connect as OAuth. Merchants can connect their Stripe accounts with you, and you can authenticate to Stripe with their details, and make charges on their behalf. You can take a fee off the top using the 'application_fee' param.
As to your first question, all users would have to sign up to and abide by Stripe's terms. They don't necessarily need to be businesses though - they could be sole proprietors.
You can find more docs on Connect here. https://stripe.com/docs/connect