No. Gifts are not taxed to the recipient, regardless of amount or whether they are from people in or outside the United States. If you make gifts, you need to check on whether you must pay any gift tax (not income tax) and/or whether you have to file a gift tax return, Form 709.
Payments made to a separated or divorced spouse as required by a decree or agreement. Qualifying payments are deductible by the payor and taxable to the payee.