One-pot synthesis of pyrazole
Excess hydrazine hydrate to neutralise the AcOH and ensure complete reaction of the diketone.

Excess AcOH to protonate all anions arising from the LiHMDS, mostly to completely protonate the anion of the diketone.

Excess enolate (and LiHMDS) to ensure all the enolate reacts. The diketone product is more acidic than the enolate and will hence protonate the enolate, so you need 2 eqs or more of base/enolate to get complete reaction.

How much NaOH for the wash at the end? More than eqs of AcOH. Don't see why they specify a base wash as everything you want to remove into the aq phase would be aq soluble anyway.