I have a questions about rollups: Do they need to be "filled" before they are posted to L1?

I have read and understand the basic concept of rollups. As I understand it, a rollup will gather a bunch of transactions on L2 to later post on L1 thereby saving on gas fees, execution time, etc.

My question is if a rollup needs to be filled before its posted to L1?

Say I have a system that collects 100 transactions before rolling them up and posting to L1, do I have to wait for all 100 transactions to be posted on my (L2) system before I post them?

What if it's a slow day and I only have 50 transactions waiting to be rolled up?

Is there a timeout where those 50 would be sent after a set time?

Do rollups get sent periodically (eg. every 10 minutes) regardless?

Is the L1 fee divided between however may transactions are sent in that batch?

Or does all of the above depend on how my system is set up?