90 day VISA-free as a a Tourist, enrolling into a school and go to Hong Kong for ext. visitor VISA

I would like to come to Taiwan with 90-days without VISA rule in late of December. When i have arrived i want to look around, tour and tourist and choose a university for studying Chinese starting from march 2013.

From what i understand, you can’t receive a proper student VISA before having studied 4 months in the school and a paper to show your attendance in class.
So my question is, if i come by 90 day without VISA - can i apply for a extendable visitor VISA in Hong Kong with the reason of study? From February i should have chosen a school and received admission papers. Will there be trouble because i came and stayed on 90-day VISA or can i come back with a extendable visitor VISA from Hong Kong to start study?

In the long run i would like to study for 2 years or even more, to become fluent in this language starting from scratch. I read that a student VISA only lasts 180 days, is this true? After having received a student VISA is it possible to renew it?