How are these little internal gear teeth made?

In the piece shown the teeth were probably cast in .

Higher precision internal gears can be cut by a multitude of processes .

Search on ' Internal gear cutting ' . Look at the images and videos rather than written descriptions .

 

My guess is that most likely that part is made with a powder metallurgy or Metal Injection Molding (MIM) process.

 

That looks more like a spline to prevent rotation than gear teeth.
It is difficult to cut internal splines in blind holds. The above two answers are both good.

In the unlikely event of the material being very hard and electrically conductive, it could be done with Ram EDM.
For softer materials I would expect it to be drop forged in a press, the same way spanners and sockets are made.
Plastic would be injection molded.

What is the material ?

 

How many do you need? If only a few, you might consider making a mould from that one with modelling clay. Modify the mould to suit your needs. Then cast one in the mould with a two part epoxy, include short fibres of something like Kevlar for reinforcing if needed.

 

Search on ' 3D printing ' and ' 3D printed gears ' .

Best again to look at the pictures before reading the text .

 

That depends on the size and the forces involved in your application, which you have not yet identified.

A coupling like that will tend to be expanded when torque is applied. That is because of the tooth face contact angle.
If made from something like epoxy, then winding a Kevlar thread many times around the outside will counter that expansion.

 

Consider the human arm. It has three major bones with ball joints, hanging from the shoulder with several muscles that change length. The geometry of the linkage has evolved into an optimised solution.
It is a mistake to transmit the full torque through a small diameter coupler directly from a servo motor. How will you link the servo to the arm and how many turns will the servo make to swing the arm through 90° ? Is it geared?

 

If this joint is just a coupling link, why not make it a square fitting to ensure robust force transmission?
As is, it does not seem part of a moving linkage.

 

Who makes the servo? Perhaps see if they have other arms available?