You can regain your welcome to the University by undertaking a Scientific Expedition or three, but I’m afraid that you would have to create a new character if you wanted to sample the delights of the second semester, as there is no way to go back to it.
As for the future of your department:
The story of your department ends here, for now at least.
Doubt Street is Shadowy content, unlocked by being POSI and having at least 110 shadowy. Speak to the urchin from your lodgings for details.
If by ‘Doubt Street’, you mean ‘Flute Street’, then keep an eye out for an academic friend asking for help - he may show up in your opportunity deck. Actual access is fate-locked though.