How to merge the middle of paths?

One more idea: Create a single Stroke Profile and flip it across it's access to get the stroke for both sides.

You could make your own brush(s) to produce the desired look. I found it easiest to make two brushes (left or right).

Color is for declarative purposes.

Good question, a few other methods you may find of interest:

QUALITY and PRECISION:

1. select all
2. Object path >> outline stroke
3. manually cleanup the paths with either the smoother tool or bezier pen tools

QUICK and KEEPING PATHS:

1. Tweak the art using the anchor point tool or width tool

QUICK & MOST FUN (in a Harry Potter kind of way):

1. Make the main stem and outline path
2. Use the warp tool as a brush with strong intensity settings and proper brush size.  Result may look more organic like a thorn bush, and not as geometrical though, so depends on  your design constraints.

You cannot join those paths.

But you can try and:

- use a round cap for the strokes and move the endpoint so it fits.

- create your own arrowhead (triangle shape)

- make a pointed cap using the wdith tool