Question

Two circles are congruent if their centers are the same

Answer 1

No, but they can be. They would be similar.

Answer 2

No. They're concentric

Answer 3

Circles are congruent if their radii are equal. All circles are similar. Circles with the same center are concentric.

Answer 4

Circles are always similar.
When the centers of 2 circles are same, that means nothing more than their centers being the same. They can be (and the probably are) different in sizes.

When circle are congruent, they must have the same diameter/radius/area/circumference.
(if of these is equal, then the rest are also equal)