afaik there is no way to “snap” the Gizmo to an arbitrary location in space. Can only snap to a vertex or to an arbitrary click on a surface.
To position the middle point to the corner use the mask, align Gizmo, scaling method.
Mask all except the middle point. ALT-click the neighbouring attached vertex (roughly where the green handle is in the first image) and drag upwards until the Gizmo axis snaps to align with the right hand edge. Then use the red handle to scale the position of the middle vertex towards the right hand edge. When aligned repeat the same process but this time ALT-click the vertex near the red handle in the first image and drag left. Scale the drag the point to algin to the bottom edge. If you want to move the attached points closer to the corner use the Zmodeler Point Action - Slide to drag them where you want along the edge.
Lot of words, sounds complicated but easily done. A very useful technique to align points along an edge or even a surface.
afaik there is no way to align the Gizmo based on a separate subtool. You could merge them, align the Gizmo as required, and then mask the second merged tool. Perform the action and then split the tool to parts again.
hth