Yes. To cater for both these instances all you need to do is create standalone recurring session (class) series for each time slot you offer with the relevant capacity. Having created one series you can then rapidly create more by using the COPY AN EXISTING feature from SCHEDULE>ADD NEW SESSION>COPY AN EXISTING.
For private sessions, if you don't wish these to be public, you can mark them as Private in the create/edit process. Once a customer has either bought something from you (e.g. a package) you can then also add them to these private sessions and debit any related package.
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