Generally no. They need to be quite fit to be able to swim in the water :)
Technical scuba divers do, but recreational divers do not.
The collective noun is a bubble of scuba divers.
Scuba divers.
dive
scuba divers
Many people use a SCUBA suit for diving. Sport divers, police divers and some Navy recovery divers.
They swim
seebees
SCUBA
they don't
Free divers do but scuba divers do not need to. Scuba divers take their air with them and would have no need to hyperventilate.
Scuba divers also wear lead weights on a belt