US Embassy is visa-free, is H4 applicable?

Applicable. As long as the visa has not expired or expired within 12 months, you can apply at your permanent residence. Through the forwarding service of CITIC Bank. How long is uncertain. Fast is two or three days, slow is two months. I once got my passport back in less than a week, and sometimes I waited more than two months to get it back (although I'm not H4). Citic means about 20 working days, which is generally faster and usually takes about a week. But sometimes it is longer. It seems that I waited for more than two months once. I hope it helps you.