Yes. “Amazon calculates, collects, and remits tax on sales made by merchants shipped to customers located in the states that have enacted Marketplace Facilitator, Marketplace Fairness, or similar laws”.
Yes, Amazon will automatically charge sales tax to customers when they checkout.
Amazon started collecting sales tax on their direct sales in Washington in the late 90s, but since have started collecting sales tax on both direct and marketplace sales, in most states. For a visual timeline, check out this page!
To sell on Amazon, you must provide a tax identification number. You can use your social security number as a tax ID, or you can also find a tax ID number on your tax returns.
Amazon requires all sellers to provide a tax ID number so that they can confirm a sellers identity, and so they can report their sales to the IRS.