Hello Francois,

Thank you for your interest in our product.

1. Is it possible to offer a quarterly subscription with a price calculated based on the number of classes in the quarter? If someone subscribes midway through the quarter, will they pay the price based on the number of remaining classes in the quarter? (This is the most important feature) - Unfortunately, currently, this feature is not built-in in Amelia. Amelia doesn't yet have a membership feature, but it will be developed as a part of the Developer license (maybe even as part of the Pro license) in the future. Please take a look at our Packages feature, and see if maybe the Packages would be useful for you
2. Is it possible to create a system in which a class is held on Monday and Thursday, with two subscriptions available: a subscription for one class per week, with the desired day selected (in this case, the client will automatically be attached to all classes in the quarter in this time slot), and a subscription for two classes per week (in this case, the client will automatically be attached to both classes of this activity for the quarter)? - We currently don't have a subscription feature built-in, but it is planned to be included in our Pro and/or Developer licenses at some point in the future. 
3. Is it possible for an employee to validate or not validate the presence of people at each class and add new unknown participants? - No
4. Will the client have an agenda with their upcoming classes and a system where they can see their payment and reservation history? - Customers can see their booking in the customer panel https://wpamelia.com/front-end-customer-panel/
5. Will the employee be able to see a summary of the classes taught by consulting the information of each class, such as the number of people and the duration?
6. Will the employee have a schedule of their upcoming classes to teach? - You or your employee can set the schedule on which days and hours will work
7. In case of cancellation by the client, is it possible to generate a gift voucher to book a unique session available in the future? In case of cancellation by the employee, is it possible for each client to receive a gift voucher for a free session? - You can create a coupon that you can send to your customer
8. Is it possible to export events? - Unfortunately, currently, this feature is not built-in in Amelia.
9. Is it possible for the administrator to make bookings on behalf of clients? - Yes
10. Is it possible to set a maximum number of participants for one class. For example, our aqua gym classes on Mondays can only accommodate a maximum of 11 people. If a person wants to subscribe, but the class is full, we want to find a way to inform them that we will soon create new time slots for people who want this activity. - Yes, you can set the minimum and maximum capacity foe each service. 
11. I would like to know if we can create an event (one-time or recurring) visible only to certain users (such as a center, for example). - Amelia doesn't yet have a membership feature, but it will be developed as a part of the Developer license (maybe even as part of the Pro license) in the future. But there may be a workaround you're interested in.
    Any membership plugin (like MemberPress, or Ultimate Member, etc.) allows you to create pages that are inaccessible to some (for example non-logged-in users). You can also create custom logic, so a user can access this page once a month (for example), but we're not sure about that, since we don't work with Membership plugins. 

We wish you all the best.

Have a nice day.