Force node to be directly beneath another node

You can enumerate the nodes before defining the edges, and then constrain node B to the same rank as node note by putting them in a subgraph:

digraph "Test" {
    rankdir = "LR"
    A;D;
    {rank=same; note; B;}
    C;

    A -> B
    B -> C
    D -> B
    B -> note [dir=back]

    note [ shape="house" ]
};

Please note that in order to have node note below node B, I had to reverse the edge direction and add dir=back to have the arrow drawn correctly.

A general technique for moving nodes around is to create invisible edges. In your case, you could create an edge from A to note, mark it invisible, and then mark the edge from note to B as non-constraining:

A -> note [style="invis"];
note -> B [constraint=false];