Your friend probably cannot deposit the check to your U.S. bank account. U.S. banks that I've worked with will not accept a deposit from someone who is not an owner of the account. I don't know why not. If some stranger wants to make unauthorized deposits to my account, why should I object? But that's the common rule.
You could endorse the check, your friend could then deposit it to his own account or cash it, and then transfer the money to you in a variety of ways.
But I think it would be easier to just deposit the check in your account wherever it is you live. Most banks have no problem with depositing a foreign check. There may be a fairly long delay before you can get access to the money while the check clears through the system.
I don't know exactly what you mean by a "prize check", but assuming that this is taxable income, yes, I assume the U.S. government would want their hard-earned share of your money. These days you can pay U.S. taxes on-line if you have a credit card. If you have not already paid U.S. taxes for the year, you should make an "estimated payment". i.e. you can't wait until April 15 of the next year, you have to pay most or all of the taxes you will owe in the calendar year you earned it.