I added a paragraph into the OP regarding opening multiple AWS accounts. I think maybe some people want to buy AWS accounts only because they think there is a rule 1 account per 1 person, but in fact no such rule exists and it's perfectly alright to have multiple AWS accounts in your name and address and even with the same phone and card number, only the e-mail needs to be different because it serves as a login.
As someone who mass produced AWS accounts for personal and professional needs I concur to all the above.
Also make sure that you keep consistent with access IP if you use the console, clean and fresh contact data (most important of course payment method).
Too many people around here offer 'tainted' AWS accounts - that is, when they offer it
That's a great point and this can actually be helped using roles. I added into the OP a mini tutorial how to access multiple AWS accounts from one single AWS account without logging into each separately.
To add, don't the AWS accounts also have to add a credit card to their account , which can lead them to get into trouble if the cards are obtained fradulently.
Yes, of course, but the problem with this is that you can't really check this. I don't know of any world-wide service where you can enter a card number and it would tell you whether the card is blocked or was reported stolen, but even if there was such a service you can't really use it because you can't see the card number in the AWS account settings. It shows only the last 4 digits. But if you buy an AWS account it's logical that you will change the card information so that you can actually make the payments (if that's what you are planning on, anyway).
This your information is very helpful and well detailed, thank you
It is also possible to avoid buying a stolen/hacked AWS accounts following this your tips?
No but it's good practice to follow when you buy one. You cannot force the seller to prove safety/provenience of the CC attached to account nor can you find out the time & place when the account on sale was created, but you can ask these questions and measure the answers along with all the other elements that the OP initially stated.
You may be able to estimate the age of an account from looking at the Bills section. There you should see the list of months since the account was created, even if the actual bill for given month was $0.