If it is possible, please provide guidance.
If WeWeb can create such a booking page, please advise on how to do it.
Yes it’s possible 
How should I handle the calendar and time?
Could you please provide some guidance?
Without diving in too deep, I imagine you would create a two rows of items which are bound to a data set for days and hours(Display collection data | WeWeb Documentation). You’d probably want to bind it to a booking backend so that the UI only displays the available time slots (otherwise you could do a static array). Attach a workflow to the onclick of each date to fetch the available times for that date and update that row of times.