can the thickness of a line be defined…so that, for example, a thick line could be draw instead of a rectangle?
Implementations must support a minimum and maximum width of 1.0. Some lamers do exactly that.
You can query the min and max width and the width granularity for aliased and antialiased lines. Antialiased widths with GL_LINE_WIDTH_RANGE, GL_LINE_WIDTH_GRANULARITY, look in newer specs for the aliased.