I have a family member which is not a U.S citizen, and nor owns any property inside the U.S. He sends me amounts of money to buy things for him here, and then send them back to him. The amounts range from 1k - 30k dollars. Will I have to pay any kinds of taxes for receiving the money? Are there any potential risks with this situation?

There are no transfer taxes in the U.S.

However, if, in aggregate, the transfers exceed $100,000 in any calendar year, you will need to submit Form 3520 to explain the nature of the money transfers.

Thank you for the help, and also if he also gifts me any money would there be any income taxes I would need to pay?

No. The recipient of a gift is NOT subject to income taxes on a gift.