How to move one edge's vertice without interrupting other mesh

Question

How to move one edge's vertice without interrupting other mesh - Here on picture, how can I make one more white vertice and slide it to the right to make 2 squares instead of this weird looking n-gons.

EDIT: Here on picture you see I have selected one edge, and it has 2 vertices. That edge seperates mesh in 2 weird n-gons. Left one is triangle(marked as "1." at picture I uploaded), right one is some weird quadrangle. I want them to become 2 squares(something as close as marked in picture "2."), obviously by adding one vertice more but don't know exactly how.

Also, how can I make edge loop to continue through this n-gon, beacuse as you can see it stopped right top of orange vertice.

EDIT: I marked with red dashed line on the picture where I want to cut mesh, but can't do it with CTRL+R. P.S.: sorry for the unclear information, but I am pretty new to Blender so I don't know proper vocabulary for those problems. Hope now it is little bit clearer.

Answer 1

Connect Vertex Path & Dissolve Edge

You don't have to move any vertices: they all are right in place. What you want is to re-arrange the topology, aka changing the connections between them. You'll need this two tools:

Use Connect Vertex Path to create an edge between two vertex

This tool connects vertices in the order they are selected, splitting the faces between them. When there are only two vertices selected, a cut will be made across unselected faces, a bit like the Knife tool; but this is limited to straight cuts across connected faces.

https://docs.blender.org/manual/en/dev/modeling/meshes/editing/vertex/connect_vertex_path.html

and then Dissolve edges to remove an existing edge:

Removes edges sharing two faces (joining those faces).

https://docs.blender.org/manual/en/dev/modeling/meshes/editing/mesh/delete.html