On/in his hand(s)

On/in his hand(s)
 

My sentence:

-When he delivers his lectures, has he any notes in/on his hand(s)?

1. Which preposition should I use?

2. Does the use of THE depend on logic and both HAND and HANDS are correct? Or is one of them, HAND and HANDS, only natural English?

"On his hand(s)" means that they are written on the skin of his hand(s).

"In his hand(s)" means that he his holding something (such as papers, cards, or Ipad) on which the notes are written.

Thank you~ Does the same thing apply to TIME?:

-He has a lot of time in/on his hands.

"Have a lot of time on one's hands" is the expression, so, yes, the same thing applies.

For the idiom with time, remember to say "time on one's hands" and NOT "in one's hands". That's just how the expression goes. :)

P.S. It's also common to say "to have too much time on one's hands".

Thank you~