Do I need another blocked account after finishing Studienkolleg and starting university?

Probably not. What you do need to get is an Aufenthaltstitel, and for that you have to meet some conditions, which varies between cities. For example, in Hamburg or Berlin you actually do need a 2nd blocked account, while in Braunschweig you need 4000 euros and a work contract. In not so big cities it's usually easier, like in Kaiserslautern you need only three months of expenses.