First of all, I do not see it from this view, I think that C1 makes the transistor operates as a common base, this is the main and the only role.
Second thing that every junction to the resonance circuit is 180 degrees Out Of Phase of each other. It seems to me you're trying to tell me that FB is done through C1, but I do not think so. FB is through the C4.
If you mean time constant, I can calc Zin (looking into the base) and find Zin*C1, but i can't calc Zout
I'm not a student, I finished my university education as an engineer in communication for years
I like to understand some of the electronic circuits prior to their implementation.
thanks