The specific price rule is applied when the date specified in the rule is the current date not the booking dates. If you want to provide discount for the booking dates, you have to use feature price plan.
Yes, these requirements are feasible and can be achieved.
But searching on the basis of occupancy, and price per person or child is not a default feature of QloApps right now.
So these requirements will be achieved via Paid Customization.
Please raise a ticket and if you want to go for the paid customization and want to discuss it further. https://webkul.uvdesk.com/en/customer/create-ticket/