Calculating Transfer Function of passive circuit
Sounds about right. However the voltage divider for Part one also needs to include the R and L of the right side of the cap. 

Zc = (1/sC * (R + sL)) / (1/sC + R + sL)

and

Vc = Vin * Zc/(Zc + R + sL)

Unfortunately that's a bit of math to go through here. Since the Rs and Ls appear to the same, the whole thing will simplify quite a bit as you walk through the math.