Let $S$ be the number of lines that can be opened, and consider the lines as vertices to form a graph $K_{\mathrm{s}}$. Label the 1983 stations as $A_{1}, A_{2}, \cdots, A_{19}$. If two lines have a common station, color the edge between the corresponding two vertices with color $C$.
From (2), every edge of $K_{\mathrm{s}}$ can be colored;
and (3), the number of different colors used on any two different edges of $K_{\mathrm{s}}$ is
$$\frac{1}{2} S(S-1) \leqslant 1983 \text {. }$$

From (1), $S$ can only be 63. From the above solution process, it is easy to see that at most 63 lines can be opened; and because each vertex of $K_{:} 3$ is connected to 62 edges of different colors, each line must pass through at least 62 stations.