Name some gymnastic events

Answer 1

Some of the events include:
Vault, in which you would naturally use the vault and you might use mats or springboards for practicing. (Used in Girls and Boys gymnastics.)
Floor, in which you might use mats or springboards for practice. (Used in Girls and Boys gymnastics.)
Bars, in which you use the bars. You also might use grips for your hands, tape, or chalk. (Used in Girls and Boys gymnastics. Girls use uneven bars and boys use parallel bars as well as the high bar.)
Beam, in which you use the beam, and a mat for practice. (Used in Girls gymnastics.)
Rings, in which you used the rings and you might use mats, a foam pit, or chalk. (Used in Boys gymnastics.)
Pommel Horse, in which you use a pommel horse and maybe some chalk. (Used in Boys gymnastics.)

Answer 2

Women's: Uneven Bars, Vault, Floor Exercise, Balance Beam

Men: Rings, High Bar, Floor, Parallel Bars, Pommel Horse

Answer 3

That would be called Rhytmic Gymnastics.