No, the travel insurance or any other type of insurances taken outside European Union is not accepted for enrolment at the university. All non-EU students (age <30) must take German public health insurance to enrol at the university.
Yes, all the existing medical problems will be covered by public health insurance.
No, you start to pay only after your arrival i.e., after semester start. The first premium will be booked on 15th of the following month of your arrival.
Yes, insurance is independent of university or the city. It is valid all over Germany. This is valid even, if you move to a different city later for internship or thesis.
As public insurances are regulated by German government, all the insurance companies must provide certain basic health coverage. Therefore, there is not much difference between each other, for more details please visit our pages: https://www.coracle.de/health-student#pricing-table
As mentioned above, the coverage remains more or less same among insurance companies. Some are bigger than other and some have good history offering cash back programs. We recommend AOK, BARMER and TK. They are well established big public health insurances in Germany.