Can aqua therapy help to accelerate my post-surgical recovery?

Yes. Aqua therapy can be a very effective post operative treatment for allowing reduced weight bearing while still exercising joints and muscles in their normal physiologic activities.
Yes in moderation. I am assuming that you had a lumbar surgery and were referred for aquatic therapy for rehab.
Possibly. Check with your surgeon first. Aqua therapy is very effective but your wounds have to be closed and healed. Ususually aqua therapy is a modality recommended 3 months or more after surgery.