A ring is a set. So is a group. At least this is how almost every working commutative algebraist views things. Category theory and its like are gaining traction but the objects are still viewed as sets.
No. It is a set together with additional structure. Without this additional structure you just have a set, not a ring.
> So is a group.
Again, no. It is a set together with additional structure.
Note: The collection of all groups is not even a set!