Do I get the visa as soon as I pay the down payment or booking?

Not usually. Eligibility depends on the property being registered so its value is recognised by the Land Department, shown by a title deed (ready) or Oqood (off-plan). For off-plan, 2026 rules reportedly let the full registered price count even with a small amount paid, so registration rather than full payment is the trigger (verify with DLD and your developer).