Hi, Moustafa 

Firstly, I would like to sincerely apologize for the delayed response as we have been experiencing an unusually high number of tickets. I am sorry that it has taken longer than usual to respond to your concern and your patience is highly appreciated.

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- Email sent when user is invited as an attendee to a private event.

Yes, you can set any custom or default notification to be sent for atendee being approved for an Event, either from back-end or front-end.

- Payment required when user is invited to private event by an employee. (Currently the user gains access to the event and is approved without payment)

- I am sorry to disappoint you, but at this time, this is not achievable with any of our built-in functionalities in Amelia.

When you schedule from back-end, it is not possible to pay by card, because Amelia does not handle payments and we don't keep any card holder data, we just integrate payment methods, for booking from the front-end.

I will pass this to the developers and management as suggestion, but please feel free to search through our feature suggestion page, 

 to see if someone may be already suggested this feature. If you can't see it, feel free to add your suggestion there, and it will be forwarded to our management for review.

After it's been reviewed it will be presented on the front page, for voting. Please note that it may take some time before your suggestion is brought up for voting since we receive quite a lot of suggestions on daily basis, and as more people vote, the feature will move higher on the priority list.

You can certainly follow our changeLog page if you'd like, where we state any changes/new features/bug fixes during updates;

and our newsletter, so you're informed about new features, bug fixes, freebies, etc.

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At this time, if employees want to book in the name of the customer, and use their card details, the only way is from a booking page on front-end.

But i understand you wish to keep these Events private.

What you can do is, you can install any Membership plugin;

and you can set that only WP users who have Amelia Employee role, have access to private pages with private Events;

and for other users you can block Access from these pages.

That is the only workaround i can think of, let me know if that can work for you.

- Addition of custom URLs below event in the event description. (I.e. Pages the attendee needs to visit, information pages, etc.)

Yes, the Event Description can render custom HTML, you can add hyperlinks.  You just have to switch it to HTML mode and edit, here is an example :

Let me know how that seems and if you have any questions. Thank you