How to use Tall Goat and other rewards?

It depends what platform you're on. In mobile, you click the goat symbol in-game on the top left. From there, scroll, and you will see your goats. For others... well, I don't know. But here's a funny use for Tall Goat: Lick people and toss them in the river. It's very easy because Tall Goat is a giraffe and the body is so high off the ground, giving you a lot of control.

You need to go back to the main menu and start a Custom Game.

From there you can add Modifiers, which change stuff in the game. As you unlock new goats, you can add them as Modifiers to change your goat appearance. This is how you activate most of the unlockable stuff.

To change your Modifiers, you will have to go back to the menu and start a new Custom Game.