Not sure what the Max Maya equivalents are but... "Poly Append" the first open border example ( result 1 face/poly ) "Fill Holes" the closed border example ( result 1 face/poly per hole ) Triangulate then Quadrangulate that face/poly This will get you at least halfway there ( divisions using border divisions )
Sometimes you can copy existing similar pieces...like for the sphere example...select a similar set of faces, copy and rotate them to the right position, weld. But in general there is no quick way to do it. Bridge or Cap and then cut/connect the edges.
what I usually do in these situations is select the line of edges that has the most vertices and then shift drag them using vertex snap, and then target weld the other ends of the edges. So in your first example, select the left line of (6) edges, shift drag snap to the next top vertex, and shift drag snap onto the right…