Is it possible to subdivide(via “subdvide” or “knife” or any other direct way) a single face without affecting its neighbours? Say for instance subdivide a cube’s face into 2 rectangles without it resulting in other 2 faces of the cube being subdivided into 3 triangles?
Short Answer: No, Blender does not support N-Gons. The closest we can get are F-Gons, which really serve no purpose but to hide edges.
However, you can always join those triangles you make into a quad and a left over triangle though.
Not the way you say it and the reason is that Blender supports only 3 and 4 sided Faces. But you can do what you say and rebuild the surrounding geometry by deleting Edges and selecting groups of 3 or 4 verts and pressing F to rebuild the Faces one by one.