# caused a deep sleep to fall upon the man

"caused the man to sleep intensely." A deep sleep is a time of sleeping in which a person is not easily disturbed or wakened.

# With the rib ... he made a woman

"From the rib ... he formed a woman." The rib was the material God made the woman from.

# This time, this one is bone of my bones, and flesh of my flesh

"Finally, this one's bones are like my bones, and her flesh is like my flesh." After looking among all the animals for a partner and not finding one, he finally saw someone who was like him and could be his partner. The man was probably expressing his feeling of relief and joy.

# flesh

This refers to the soft parts of the body like skin and muscle.

# She will be called 'woman,' because she was taken out of man

The translator may want to write a footnote saying "The Hebrew word for 'woman' sounds like the Hebrew word for 'man.'