How does the Steins;Gate phone microwave work?
I will leave out anything that is related to further in the anime.

1- they went green because they entered the blackhole that was created, but were spat out again in the same place as no "space/time coordinates were sent (ie a phonenumber)

3- as far I can tell it is always needed up until Okabe does something "different".

4- it is in a dock stand probably hard wired manually into the circuitry on the microwave

5- lazy animation

6- date time

8- PLOT

Quite easily, as long as they know the phonenumber as pagers worked alot like texts do these days.

12 - Cathode ray tubes is what Old Televisions used to create images, I wont go into any detail so google this.