Can I use my home address as the business address for the license?

That would be fun, but you would to have proof. Plus, if the amounts are not material it may lead to nothing.

You can use the gift card to buy products and services anywhere in the United States as long as the merchant accepts American Express credit card payments.

Both of those options will work, although including the unit number on the street line is preferred.

I have the same problem, I wrote to Groupon and told them that I will ask my credit card company to charge back if they do not resolve this issue....

You have to. And your license (once received) has to be in view inside the business address.

Yes.

If you sell them on places like Etsy, you won't need one. If you want to sell them on the street, check your city's vending rules.

No, using payments in Messenger to handle your business transactions will get your payment privileges suspended.

You should consult your municipal government department advisory department in order to find someone's license.

Speak to your local city hall about acquiring a business license with limited liability (so that parents can't sue you for your own personal assets). After all, private schools ARE...