The Cascade badge raises the speed of all your Pokemon
You do not need the move Cut to earn the Cascade badge. Gaining the Cascade badge allows the use of Cut outside of battle. The Thunder badge can only be earned after teaching a pokemon the move Cut.
In cerulean cities gym you must beat the leader misty to get the cascade badge.
The Cascade Badge
I don't think there is such a thing as Cascade Attack.
The boulder badge, the cascade badge, the thunder badge, the rainbow badge, the soul badge, the marsh badge, the volcano badge and the earth badge.
Cerulean city
you cant trust me
you can't put badges on Pokemon
The 8 badges for Pokemon Red are: Boulder Badge, (Brock) Cascade Badge, (Misty) Thunder Badge, (Lt. Surge) Rainbow Badge, (Erika) Marsh Badge, (Sabrina) Soul Badge, (Koga) Volcano Badge, (Blaine) and Earth Badge. (Giovanni)
* Pewter Gym - Rock Badge * Cerulean Gym - Cascade Badge * Vermillion Gym - Thunder Badge * Celadon Gym - Rainbow Badge * Fuchsia Gym - Soul Badge * Saffron Gym - Marsh Badge * Cinnabar Gym - Volcano Badge * Viridian Gym - Earth Badge
Badges have passive abilities. Just having it activates any abilities it might give.
To obtain the Cascade Badge you will need to defeat Misty the Cerulean City gym leader in a pokemon battle.