Does Jester's Mom Send Her Money?

She has been very free with her money, sending Jester away from Nicodranas with five thousand gold and sending another two hundred gold to Jester later in Zadash.

Is the gentleman Jester's dad?

In "The Threads Converge" (2x85) it was revealed that the Gentleman was her biological father.

Does the gentleman know Jester is his daughter?

Jester now knows that Babenon Dosal, her father, is indeed The Gentleman. The Cobalt Soul is well aware of the Gentleman; Expositors had contact with him before Beauregard Lionett did, though Beau's entries are particularly important.