Can I hold an umbrella over the player or block the sun while they play?

Not while the stroke is being made. A player must not make a stroke:

• while getting physical help from you or anyone else, or
• with you, another person or an object deliberately positioned to block out distractions or give protection from the sun, rain, wind or other elements.

Allowed:

• Holding the umbrella over the player before the stroke, and stepping away before they swing.
• The player protecting themselves, for example by wearing rain gear or holding their own umbrella.
• Asking someone who wasn't deliberately positioned by the player to stay where they are or move (for example, a spectator casting a shadow over the ball).

Penalty: two strokes for your player in stroke play (loss of hole in match play).

Source: Rules of Golf (2023), Rule 10.2b(5).