b) The second system is reduced, not consistent and therefore has no solutions. You did not need to say anything else.
c) The third system is NOT reduced. This was an error that several people made.
The coefficient of y in the second equation is not 1, and the column of y has not been cleared. Likewise, the column of z has not been cleared. Once the system is reduced, each leading variable occurs in only one equation, and with coefficient one. If the system is consistent, then there is exactly one leading variable for each nonzero equation (i.e., each equation that is not 0 = 0).
In the second problem you were asked to carry through the reduction of the system. You should subtract 3 times the first equation from the second and then write BOTH. The first step in reduction produces
x+y+z = a
0 = 6-3a
Unless you wrote down both of the above equations as a system you did not receive full credit.
The second equation shows that the system is inconsistent if a is different from 2 (no solutions in that case). If a = 2, there are infinitely many solutions (the second equation becomes 0 = 0, while the first now has one leading and two free variables).
It is best to answer all parts of the question explcitly, so you should also say that there is no value of a for which the system has a unique solution.