This is a question all about "how do I specify/size my equipment," so I think it's probably a fair question for the site, though it is close to an open-ended design question.
Regarding the "how do we choose" portions of questions 1, 2, and 4 - you have to have some kind of a test procedure. Why are you making the arm? What is it that you're intending to test? You mention resonant frequency, but do you mean the structural resonance of the arm or do you mean the plant resonance of the arm+feedback+controller control loop?
How are you intending on performing this test? Are you going to add various weights to the arm and repeat a particular test, or are you going to vary supply voltage to the actuator, or something different?
You'll have to determine the static torque required to support the arm (and test load?), the dynamic torque required to accelerate the arm (and test load?), and estimate a top speed at which you expect to operate. With a torque requirement and a speed requirement you can calculate a power requirement. Motors have some efficiency (listed on their datasheet, but I would use 70% as a thumbrule) so you'll need a power supply capable of providing the motor with the electrical power needed for the motor to provide 70% of that as mechanical power.
Regarding the torque sensors and rotary encoders - again, just like the motor datasheet will give you the actual efficiency for that motor, the sensor datasheet will tell you what the capabilities and limitations are for the particular sensor. This typically includes measurement range, number of revolutions you can turn the sensor, supply voltage, output format, scale factors (how the output format relates to the measurement range), accuracy, etc. An absolute rotary encoder is anything as simple as a potentiometer, which would output a variable voltage, up to a optically isolated high resolution encoder that outputs Grey code on some high speed bus format, and everything in between. Where do you put these sensors? Wherever you want the data. If you want torque at a joint, you put the sensor at the joint. In order for a torque sensor to register a torque it needs to have a torque applied to it, which means that they are typically some load-bearing component in an elbow/joint design.
Regarding the power amplifier - A microcontroller is only going to provide power in the milliwatts region. A computer/USB port may provide a little more power, but probably not enough to drive a large robotic arm. You'll need a device capable of converting the control signal that is outputted from the microcontroller to a variable power source that will be the input to the arm actuator. The variable power source is your power amplifier, and again the size you need is determined by however much power you're expecting the arm to use.
Regarding the step input - you give a light a step input every time you flip a light switch. The supply voltage is 0 V, and then suddenly the supply voltage is 110 V or 220 V. You can give a step input to a motor by applying a voltage to that motor, and you can provide a step input to a controller by providing a reference to that controller.
Finally, maybe you're noticing that this is going to be a lot of work. I would fully expect you to go through 3 or more design iterations. You design an arm of a particular size and shape to ballpark the motor size requirements and find a torque sensor and rotary encoder that also meets your needs. Then you revisit the arm design to try to allow it to attach to the sensors; this re-design may mean that the weight of the arm has changed, which means you get to re-select the motor and sensors you use. This process repeats until your solution converges.
power amplifier.... more common term ismotor driver$\endgroup$