I know the algorithms, but i still don't know how to approach the questions
Allright, if I read this correctly here is what I think it should do (Some parts are possibly missing or badly formatted, but the following should make sense):

You basically copy your graph 4 times into different layers. Let's call them L1,L2,L3,L4

In L1, the highest Layer, every connection from the original graph instead goes down to L2.

From L2 every connection goes to L3, and from L3 to L4

Finally L4 looks like your original graph.

So if you search for the shortest path between u and v with at least three edges, you start at u in L1 and want to end at v in L4

Since you can only move down 1 layer at a time, you need at least three edges to reach v.

Take this graph as an example:



Let's assume we want to move from the left to the right, and the upper connection is the 

shortest one. Then the correct answer is still to move through every other node, because taking the shortcut uses too few edges.

If we convert this graph we obtain the following:



Here we want to reach the bottom right from the top left. As you can see, finding a solution in this graph, automatically gives us a solution with at least three edges.

Note: Sorry that the vertices are not labelled, could not figure out the text function in the drawing tool I used :/