Does this feature exist

Hi!
I have an idea of a WordPress site I want to create. I want it to have teasers of “events” on the front page that can be sorted with a search. I also want each of these events when you click on them, to display a calendar where you can book certain days for the happening.
And when the days are fully booked those days can not be booked anymore.

Is this possible?

All the best
Elina Tyskling