Hi Noman,

thank you for taking interest in Amelia, and for reaching out to us!

•  We have a Customer Panel, where customers can manage their appointments and events - if you give them permissions, they can reschedule or request cancellations.
• For the event booking form - this can be made with adding Custom fields to the booking form (name, email, and phone are standard fields; you can add more fields for, for example, dog's name, breed, etc).
• Unfortunately, at the moment there's no option to set recurring payments aka subscriptions in Amelia itself. One of the reasons is that Amelia doesn't store any payment details (what makes it so GDPR-friendly, on the other hand). 
  We are always looking for ideas on how to make Amelia better. So if you have a couple of minutes, please suggest this feature on our website. Probably, it can be achieved with some third-party plugin or service, such as WooCommerce's Subscription, but we didn't test it with any subscription plugin, that's why we can't be sure if it will work flawlessly. Our integration with WooCommerce is payment based, however, for now, only for single transactions.
• Space booking can be rented for any time span within 24 hours; for daily rents, you can set up a Daily recurring service for renting - your clients would pick a first day, choose to repeat it, and then choose until when they will rent.

I hope this helps, Noman