I'm no expert but this is what I've done and what I think I know.... lol

It is super easy to apply and get a business license. I'm in Washington state and I visited the states Department of Revenue site (just google "your state dor") and you can apply there. It cost about $100 in WA and some online forms and you got a business license. If its just you working for yourself apply as a sole proprietor, if you plan on hiring employees apply as an LLC and you'll get a TAX ID number. If you're a sole proprietor you can use your SSN as your TAX ID number.

Drop shipping I don't know a lot about but I've heard of a couple ways of doing it. (I think this is against eBay rules but...) Some people will have Amazon Prime account (2-day shipping) and basically list things on eBay they find on Amazon and offer fast shipping. When someone buys it... You enter the eBay buyers shipping information on the check-out on Amazon. I feel this is kind of shady, I've never tried. A friend of mine does it and he's been burnt a couple times like shipping to AK or HI when the person from Amazon doesn't ship to those places.

Another drop shipping method is using a company. There are several companies out there that if you sign up with them they'll offer things for you to sell from their website and when someone buys it, you give that drop shipping company the buyers information and they send the goods. Sounds easy but from what research I've done it's not worth it at all. You don't make a lot of money and some companies are shady. Always check the BBB reviews or any other reviews before you sign up for something like that to avoid any scams or other problems.

Anyway, That's about all I know. Good Luck!