As a comment to your question says, you don't need a 3rd current limiting resistor and the two resistors will limit the current themselves if you are still worried. You should also read Rohat's answer about debouncing the switch. 100nF across R2 should do it.

Is GH a short or is there an error in the diagram?

Have a look at electronics-tutorials.ws/transistor/tran_1.html The relationship between alpha and beta is given about half way down,

Have you done any research into this question? Have you looked up the definitions of alpha and beta? Having done so what don't you still understand?

@PeterBennett Agreed, just think of what happens at the extremes of travel of the wiper. At one end the input is shorted to ground, at the other it is connected directly to the base of the BJT with no apparent current limiting. I imagine the diagram is incomplete. There is no DC biasing for the BJT and no AC coupling for the signal.

@comandantexd OK, so no long and / or thin bits of wire in any of the power feeds and the PSU and the Arduino are fed as independently as possible,

Do you really need the 16 off 1N4007 diodes which are 1000V 1A rectifiers when a general purpose Si diode such as the 1N914 ans it's brethren are considerably cheaper?

This looks like a homework question, and we don't do homework on this site. If you specify exactly what you don't understand, I'm sure someone will help you. For a start, using Kirchhoff's Laws write down the 2 equations for the left and right hand loops letting current i1 and i2 flow through the 10 and 20 ohm resistors respectively. You now have 2 simultaneous equations in i1 and i2 you can solve with simple algebra.

The short answer is - yes. This question has been asked and answered several times, notably here electronics.stackexchange.com/questions/93452/…