6013 is indeed a drag rod. You do not use a whipping motion. And you
should not weave more that about 2-3 times the diameter of the filler
metal.

6013 should give you a beautiful weld. The reason you are getting
inclusions is that you are moving the puddle back over flux that has
already solidified. You can get away with this a bit with a rod like
7018 which is more penetrating, but not with 6013 which is designed for
sheet metal.

The way to get equal length legs on bot plates is to favor the top
plate. Instead of your electrode splitting the angle between the two
plates, it needs to be laid a bit down toward the bottom plate so that
the tip points more towards the vertical plate than the bottom plate.
Gravity will bring the molten pool back down towards the bottom plate.

If a simple drag motion does not make a big enough bead, just make
multiple passes.