Answer:
You will find me with four legs, but no hair. People ride me for hours, but I don't go anywhere without needing to be tugged. Jerked or turned on, I always manage to be ready for work.
What holds names and memories which are not its own?
When they are caught, they are thrown away. When they escape, you itch all day.
What has a mouth but can't chew?
What turns from red to black as soon as it touches water?
They are many and one, they wave and they drum, Used to cover a state, they go with you everywhere.