Deriving the S-parameters, different Matched Loads possible?
It is possible to define S-parameters for networks intended to be used between systems of different impedance, for instance transformers or pads intended to work between 50 Ω and 75 Ω systems.
However, when you are asked without further clarification to compute the S-parameters of a network, you should assume it's being used in a 50 Ω system.
There may be many practical reasons a network does not present a good match to a 50 Ω system. Perhaps it's actually intended as an antenna match.
Regardless of what actual impedance a 2-port is intended to present, and regardless of what terminates the other port, the S-parameters can be combined so that the measurement in the 50 Ω system can be used to design for other impedances.
You are not being asked to compute the system impedance of this particular network. What you are being asked to do is
a) Terminate port 2 in 50 Ω
b) Drive port 1 with a 50 Ω source
c) Compute S21 as the ratio output/input
d) Compute S11 as the ratio reflected/input
e) Swap ports 1 and 2, and do the same for S22 and S12