Computation of the Scattering Matrix of a Transmission Line
why is port 1 closed on Zc1 and not to Zc?


Because in the problem statement you specifically said you wanted, "scattering parameters normalized with respect to an arbitrary impedance Zc1, which is different from Zc".

To test (or simulate) the scattering parameters of a network normalized to an impedance \$Z_{c1}\$, you terminate it with the impedance \$Z_{c1}\$.


  if we close port 1 on Zc1, it will be non true that a1 = 0, from my point of view.  In fact, there will be physically reflection, since there is an impedance mismatch between the load Zc1 and the transmission line which has characteristic impedance Zc.


You are correct there will be a reflection there. But this reflection is only within the transmission line being tested (the DUT), so it is not considered as part of the wave \$a_1\$.

Imagine you replaced the termination \$Z_{c1}\$ with a length of transmission line of characteristic impedance \$Z_{c1}\$, and terminated that with the impedance \$Z_{c1}\$. As far as the behavior of your DUT is concerned, this would not change anything. But it would be clear that there is no forward travelling wave \$a_1\$ in this transmission line. The reflection is entirely within the DUT, not in the termination.