Buffer Intersection

Some suggestions you could try:

For step 3:

-custom ‘HorizontalAngleCalculator’ for each line then calculate the differences to get the smallest angles

-’Intersector’ (you can add a tolerance here, so no buffer needed beforehand), this transformer creates a node at the intersection

For step 4:

-’NeighborFinder’ (‘Insert Vertex On Base Feature:Yes’) with line and new vertex from step 3 as input

-VertexCreator for nearest base/candidate and ‘LineBuilder’

For step 5:
this could be tricky, but I would try to create a 4m long line and then rotate it with given angles

Attached is a simple way, might be too simple, depending on how straight your lines are.

Offset the lines, then intersect them. If they’re straight and meet at the point, they will only intersect with each other at three points. The furthest of these three points will be on the angle where the two lines are closest. The NeighbourFinder attributes then tell you the coords/angle/distance of this vector which you can place your point along.