Electronic – Is it possible to determine load on a stepper motor when stopped

One important factor when working with stepper motors is hold torque. You can do some simple calculations based on your camera weight and platform radius to determine the torque due to gravity, and your hold torque should be a fair about larger than that or the motor will slip. You'll also need stepper motor drivers in order to control the motors and provide enough current as well as the proper signal to control the motor. I've had experience with the Pololu A4988 I'm conjunction with Arduino; it's simple to use and only used 2 digital IO pins (at minimum). You can also spare more pins and control things like the driver enable, etc. As for actually choosing a motor, that can be tough. I'd pick a price range and form factor that you'd like to be within and use that to narrow it down. I'd also stay away from the spark fun motors as they are usually on the more expensive end and not the best bang for the buck.

Your understanding of slip rings seems correct.

There are many companies that make slip rings. So answering specifically to those is 'off-topic' for electronics.stackexchange. You might have to read through several pages of web-search results to find them.

Typically, slip ring costs increase rapidly the more separate contacts you need. So 4 power signals for one stepper motor, and two for the inner motor might be much more expensive than only two for power. It may also cheaper and easier to get a multi-circuit slip ring with two 'power' connections (for power and ground) and several 'data' connections.

Edit: One use for slip rings is connecting the buttons and airbag on a steering wheel to the rest of a car. So automotive slip rings are a mass-produced; they would be a low cost, relatively robust part. So you might find something to experiment with from a car 'junk yard'. It might be low-cost to get something there, and experiment with it, before trying to find 'exactly' what you need.

You might consider putting the control electronics 'on each motor', so that you only have to get power and ground through the slip rings. Then the electronics 'on the motor' would use that power to drive the motors power connections.

So the first/outer motor would be connected directly to its controller.
Power and ground would be fed through a 2 power-circuit slip ring.
The controller on the second/middle motor would take power and ground, and convert that into a signal to drive the motor.
Power and ground would be fed through a second 2 power-circuit slip ring. The controller on the third/inner motor would take power and ground, and convert that into a signal to drive the motor.

I assume the electronics on each motor would need to understand its position. That might be done using a gyroscope sensor on the motor controller, or use a low-cost radio.