Can I use this sign to mean 'hold on' or 'wait'?
No, if you mean 'wait a moment,' you should use the specific sign for 'wait' (wiggling fingers with palms up). This sign is strictly for physically holding or gripping an object.
Does it matter which hand I use?
You should use your dominant hand to perform the 'S' handshape and gripping motion, as it represents your primary hand doing the active holding.
How do I show that I am holding something very tightly?
You can emphasize the sign by squeezing your fist tighter, making a sharper downward motion, and using a strained or intense facial expression to show the extra effort.