There is no limit to the amount of remittance acceptable in the United States. However, each remitter (not limited to parents) shall not exceed 10000 USD at a time, and the total remittance amount shall not exceed 10000 USD every year. If it exceeds the bank, it must be reported to the government, and you may be asked to provide the source of remittance funds to prevent money laundering.
3. The payee does not pay personal income tax. (Only after receiving a remittance of more than $5 million in a lifetime)