You can add players and leave their names empty to get that effect.
Yes. This is what I do. And this is a lame workaround. There should be a simple "No. of Players" box you can simply enter a number into (or simply ignore, if you don't track player count).
Player count and location are the two things I track when recording plays, and hitting "add player" multiple times (but leaving the fields empty) is a stupid waste of time.
Don't get me started on whether the idea of logging plays itself is a stupid waste of time