I am the footprint of a falling drop, growing larger long after it stops.

I get smaller every time I take a bath. What am I?

Where I come from is not where I'm from; I'm only around when my source is not found. I am most active when you are at rest; You'll say it's dark but I'm doing my best.

You should keep me on, or you may get no service. You can be a stuffed one, though that is not nice. If you are in need, I may give you the one off my back.

Since my spelling is questionable today, here is one even a kindergartner could spell correctly. What is small and furry with sharp teeth and nine lives?