Hi Salim

Thanks for detailing some of your requirements - I will describe how this could be achieved withing Totara 

1. Calendar - the Teacher/Tutor should only see his/hers events and activities (Seminars) where they are planed for.

if you require a seminar that a trainer is responsibe for the in the Seminar settings under Calendar options select None to display on a trainers calendar seminar activity events will only be displayed as User Events on a confirmed attendee's calendar.

2. The Enrollment into a Course needs to be approved by a Manager.

If the course includes only seminar activities then in the seminar settings there is an approval workflow available

If it is course approval with other activities then adding a learning plan enrolment restricts users only enrol in a course that has been approved in a learning plan 

3. Manager should be able to recommend courses to a student with a click or share button. And if possible "prebook" a course for a student.

This is more in the Engage area which has likes and also a recommendation engine. I am not sure what you mean by prebooking a course can you provide more detail?