As the second person of the "we", I would like to add:
A legal consultation I had confirms: Impressum is a must.
Further remarks regarding the above mentioned possibilities:
* Running the website via University: If this means running it on the Uni server, it might also affect the initial developer’s/operater’s/researcher’s legal position towards the site, meaning: University might claim certain rights on the project.
* Having your name + work address in the Impressum: „You probably need permission by the university, We did not find any cases/reports on the question if this is in line with the laws or other regulations that apply“
In a legal consultation I was clearly advised to seek this solution, in order to avoid to make my private address public. However, checking your Uni postbox regularly then is advisable.