How to reuse animations on different people?

So say i make a person character and then go through the animation process to make him walk. Then I make a woman and I want to make her walk in a similar way but maybe earlier, or 5 inches to the right, or something like that. Is there a way I can say “apply this animation to THAT character”?

That depends on how you animated the character.
If you used a skeleton layer or some other sort of rig, then you can “simply” remove the previous character and link the parts of the new character.
If you have animated the shapes and splines directly, I don’t think there is a way to transfer the animation

If I animate one character with a skeleton, and then copy-and-paste/duplicate it on top of another character (and link it), wouldn’t they animate at the exact same time (like synchronized swimmers)? Is there a way I could make it animate at a later time?

Furthermore, could I make one character walk 5 steps and another walk 18?

Take a look at the time loop and the free time layer for that.
Also if you make a copy of the whole file and edit one copy of the file to contain the other character, you can animate them independently.