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Most of that is answered about 15 posts up from yours in the DS4 PCB Scans thread. https://www.acidmods.com/forum/index.php/topic,43542.msg326641.html#msg326641You're not going to be able to mimic the Analog (sensitivity) function of them with an Arcade button as it's more of a Digital device, it's only off or on, so all you'll get there is no Trigger pressed or full Trigger pressed. You would have to use a completely different kind of button to keep that Analog feature.
It wouldn't work the way you have it. You need the 2 Pull-Up Resistors installed in there, and when the button is pressed it will go full throttle.
There is no reason to duplicate the circuit completely, as you're using a Digital button, so the Resistor that is the actual R2 is not needed. Half of R1 is the 3.2v, not ground, so that Resistor is a Pull-Up for the R2 line. The Pull-Ups are 7.5k, and how you need to install them and what buttons uses what for it's common is explained in the other thread.
Yes, that will do it, but it's 7.5k, which is 7,500 ohms, not 7.5ohms. You can use the 10k there instead of the 7.5k though. R2 is the R2 button line, 2R is just the common for the R2 button line. The Triggers don't work like any of the other buttons.