Is there a ruling about what should be done with?
1) The abdominal cord of a new born baby, after it dries and breaks away? 2) Shaved hairs of a new born baby?People say that they should be thrown away into the sea, and not in the garbage (or unclean places), otherwise the Satan will affect the baby thought it. Please advise, with any Hadeeth, if available.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

Some scholars are of the view that it is desirable to bury anything that is taken from the body of a human being, hair or any thing else. So the abdominal cord that you have asked about and other things are included in this. Anything that is taken from the human body should be honoured and not merely thrown away. No scholar has ruled that they should be buried at sea, and there is no evidence that Satan will affect the new-born if his hair and abdominal cord are thrown away. This is superstition or myth.

Allaah knows best.