Suggestions for class registration and payment

I am new to stores/payments and I have a client who needs to have users be able to register for classes and pay for them on her website. Originally I thought I would use woocommerce, and although that could work out (with custom form field add on and mailchimp add on), it seems redundant to have to enter classes both there and in my calendar (I am currently using Time.ly event calendar and like it however their “ticket” option doesn’t allow tickets for events that repeat, and most of the classes are 6 week sessions, so unfortunately that won’t work.) Ideally it wouldn’t use the term “ticket” either because it’s more of a registration but that isn’t as important as being able to:
1. Enter event details that include an option to register and pay
2. Have those events populate to a calendar to display on calendar page…
3. …with the option to have a feed in the sidebar
4. The registration would have the option to customize form fields
5. .. and would be nice to be able to opt in to Mailchimp

So am I dreaming? Is there a plugin out there that does all that or suggestions for a way to accomplish it (or most of it?). Any info is greatly appreciated.
Thank you!