Snapping functions can’t snap to the intersection of the transform and the snapping element normal, unless it happens to be in 90° angle, which is useless.
Would either have to cut with the knife (K) for example to give another suitable snapping target, or use different cutting options to make the form
The second one is easy. Face snapping in object mode, with rotation option enabled. Could then offset the object by moving it along the object’s local axis. That’s done by having transform orientation set to global or local from the header and then pressing the axis key twice: G, Z, Z moves along local Z. With manipulators that needs to be set to local.
Theres too some addon you can utilize for somplify it ( snap CAD addon, snap utiliese etc ) … Some are free, some are not… i let you do a research on Blender Nation .
Theres too some addon you can utilize for somplify it ( snap CAD addon, snap utiliese etc ) … Some are free, some are not… i let you do a research on Blender Nation . But as it is, i think JA12 have nicely show you the workflow for it