Marcel answered most of your questions, already
3) I'd like to implement a sort of department admin and survey administrators under a department admin. Survey administrators can only manage their own surveys. Surveys created by survey administrators are automatically tied to their department. The department admin can only manage surveys created under their department. I imagine this will be an addition of a department model, changes to the survey model and the admin user model. Is there a mechanism for such right now? Or do I have to write it myself for now?
From my point of view this sounds like an additional level that has to be added to the general Limesurvey right module. Since that affects nearly every feature because the rights details have to be adjusted and to my knowledge there is no existing mechanism for this, I wouldn't want to touch this.

I think 'user roles' would be an important addition to the user model in LimeSurvey - so if you want to go the full way then re-designing user groups as user roles would be a good thinkable way which could be part of the future core application.

On the other hand if you want to have 'just' a quick solution then implementing your own permission concept using a plugin would also do.

Best regards from Hamburg/Germany

Carsten Schmitz

LimeSurvey Project Leader