How can I reduce swelling after arm & hand surgery?

Depends. You should always expect swelling after surgery. The amount will depend on the surgery itself, the patient, and how aggressively the hand is being used. Strict hand elevation, wrapping, and anti-inflammatories (only if ok with your surgeon) can help minimize swelling. Hand therapists can also be very helpful in controlling post-operative swelling.
Depends. Some amount of hand swelling after hand surgery is normal. The amount of hand swelling depends on the condition and the treatment needed for the condition. Is important to control the swelling mostly with elevation and keeping the fingers moving. If this fails occupational therapists can help to reduce the swelling.
Swelling can occur. but ICE, MOTION of the fingers and whatever is allowed, ELEVATION, gentle not overhead but higher than ones heart are huge in reducing swelling. IF allowed make a full fist and fully extend the finger but check with surgeon as to what is allowed and not allowed.