I am a green card holder. My father is neither a citizen nor a resident of the USA. He has been saving up money for me and sends it to me every 2 or 3 months sometimes over $10,000. The money he sends me, is it taxable? And o I have to register it with the IRS or something?

You will not owe any taxes on the transfer; neither will your father. However, you probably will have to submit Form 3520.