In USA, on Check you cannot write "To the payee only" as in Israel or "account Payee only" as in India.
In USA it is assumed that the Bank will verify that the name matches with the person cashing the check.
I understand that basically you want that check to go to an account rather than being cashed, I don't think that can be limited by writer. So if you ...
For example, if the envelope is lost in the mail and the check arrives
at some stranger's hands, how do I guarantee that person cannot use
(deposit, transfer, cash) the check?
You need to minimize the chances of it getting lost. In the United States the USPS has certified and registered mail. Certified mail requires a person to sign for the letter, ...
You can't really, it's the bank's job to do that. That's the whole point of writing a name on the For line. Banks aren't supposed to accept checks endorsed by someone other than that person. When you get your canceled check images (or the actual checks if your bank still does that), you should be checking that that the depositor is who you wrote the check to....
Yes he can.
For 10K form 15A,B is not required.
It's not during transfer, an affidavit on stamp paper; however for such amount it can be a simple piece of paper as well.
Under liberalized remittance scheme upto USD 250K per year.