1. Are we talking about drafting dimensions or sketcher constraints? My responses above are based on sketcher constraints. If we are talking drafting, there is a Dimensioning Toolbar that lets you choose the dimension direction. (see first attachment below)
2. Your last image doesn't show the contextual menu, so I'm not sure what you see. When I right-click when creating a new dimension, I get a contextual menu that let's me choose FORCE HORIZONTAL DIMENSION. (see second attachment below) Be careful when using an Auxilary View: "Horizontal" might not be the direction you want. You might want to use the FORCE DIMENSION ALONG DIRECTION and choose a reference line.
The contextual menu you're looking for is only available during the construction (or definition) of a constraint. Once a constraint is created, a different contextual menu is available to edit the constraint as it was defined.
View attachment 495
So, you should right-click immediately after the constraint is first shown (and before you left-click to position the constraint).