A small mousepad makes your keyboard slide. Get a desk mat.

Yes, for both questions. A standard mousepad under just the mouse leaves your keyboard sitting on the desk, where it can slide around from normal typing. A large desk mat with a rubber or silicone base will keep the keyboard planted.

The physics is simple: rubber grips, bare desk doesn’t. A small mousepad only covers the mouse area, so the keyboard has no traction. A full desk mat gives the keyboard something to bite into, and the weight of the mat itself helps too. Just make sure the mat actually has a non-slip bottom—some cheap ones are just fabric and will slide almost as bad as the desk.

I use a $30 wool felt desk mat with a rubber backing and my mechanical keyboard hasn’t moved in years. Worth every penny if you hate chasing your keystrokes.

You don’t need to spend a lot, just get one with a proper rubber base.