Writable area on a PCB

Assuming white silk screen, just draw a solid box on the silkscreen layer.

You can then write on it with a permanent marker.

Here is an example from a board I made a while back:

That was before I wrote on it.

A common practice is to leave a square area on your PCB, filled with white silkscreen as a background. If you would like to write on the PCB with something other than a permanent felt marker (e.g. a ballpoint pen), a paper adhesive label could be placed over-top of the area.

If you use an adhesive label, make sure that it's applied after reflow/soldering.

Yes. You can write on basically any part of a PCB with a permanent marker. If you want, you can also use your silkscreen layer to provide e.g. a white background, or checkmark boxes etc.

This is pretty common, eg. for boards that go through manual QA.