The dancer says she can't make it, then picks another group of the course or an open class that fits your rules. Her own seat is free again for someone else.

Another group of the course, an open class, or both. Same style only, if you like.
The same level by default, or one level either side.
A window of days either side of the missed week.
A limit per block, per dancer, so blocks stay blocks.
No email, no office hours.
The empty place can go to somebody else.
Nothing for you to add by hand.
She can take an open class instead, if you allow it. If nothing fits yet, her window stays open.
Then there's no catch-up. Telling you is what frees the seat, so it's what earns the week back.
No. Both rosters update on their own.
Put your Tuesday beginners on Dansly, leave everything else as it is, and see whether anyone still has to text round.