AC condensing unit + pressure switch

Given this:

"I eliminated the pressure switch #2 and it did work.

1. Can I run the system without the switch for now?
2. Are the switches replaceable as it seems to be installed there permanently (from what I can tell).
3. As Moe mentioned, could there be a defective pressure the would not let the voltage through the switch? "

You're at the end of your options. You;ve determined it's the pressure switch that is preventing the compressor from running. That means either:

A - The switch is bad

B - The switch is OK and there is a problem with the system pressure.

Either way, you need an HVAC guy. And I would not run it bypassed, unless you want to run the risk of additional damage.