I encountered with a problem when I read the part of Enriques-Babbage Theorem of the book Geometry of Algebraic Curves Vol. I by ACGH. It is stated on page 112-113 that all subsets of $m$ points of a hyperplane section $\Gamma=H\cap C$ of a curve $C\subset\mathbb{P}^r$ impose the same number of conditions on a linear system $\mathcal{D}$ on $C$.

My first question is what the definition of the number of conditions on the linear system $\mathcal{D}$ is.

In the proof of Proposition 3.1 of Chapter III, a hyperplane section $\Gamma=H\cap C$ of a canonical curve $C$, which consists of $2g-2$ points, together with a point on $H$ outside $C$ form $2g-1$ points in general position that impose $2g-3$ conditions on quadrics by the Uniform Position Theorem. How is the number $2g-3$ obtained? How is the Uniform Position Theorem applied?