I would need a Drupal module where authorized users create "events" and
authenticated users can book for it.

here's an example:
A therapist works in different locations (cities or associated studios) at
different times, he has to be able to provide its clients (site users)
some range of time, from-to, clients can book for 1,2,3,4,5,etc hours as
well as all the day, Therapis can now chose a client or another, while not
yet confirmed a time have to be available, as soon as appointment is
confirmed it have to results as booked (without showing who booked it).
At the end user can see a summary of his own booked appointment (both in
the past and in the future)

so:
Therapist says he works:
May 15th from 9am to 4pm in New York
May 16th from 8am to 1pm in New York
May 24th form 11am to 7pm in Rome
June 1st from 1pm to 11pm in Toronto

Users can book 1,2,3,4,etc hours or all the day, as soon as they booked this time, Therapist receive an email with this request, more than one user can request to book it, as soon as Therapist accept userA or userB this period will result as "Booked" so that other users can't try to book it.

After booked this time, user has a summary with his past and future appointment.

User can chose to receive a confirmation email, by default this is disabled.

Send me an economical and time proposal

Take in mind that timezone have to be the site one I guess you can use Views2 in some ways and I have to be able to translate this module in different languages.

Something similar to Public Booking that look like not working.

Contact via Contact tab only.