By the Brill-Noether Theorem, a general curve $C$ of genus $g\geq2$ has maximal Clifford index $\lfloor \frac{g-1}{2}\rfloor$. Hence a very naive question is:

(Q1) Is a curve with maximal Clifford index a *general* curve (in the sense of Brill-Noether theory) ? And if not, what can be said about such a curve (when non-general) ?

Of course a similar setting holds by considering the gonality instead of the Clifford index, but I guess that in this situation the two are completely equivalent, that is:

(Q2) Is the gonality of a curve with *maximal* Clifford index $c$ always equal to $c+2$ ?

Edit: by curve I understand an irreducible curve.