Can I use two arduino output pins to simulate a RS422 trigger?
A) it should work. It should also work with one GPIO pin if correctly biased. You could use Arduino, but you might have an XY problem, if you are looking for ways to test this but have already chosen to do it with Arduino. It could perhaps be simpler to get a waveform generator so you don't have to build or program anything.
B) Of course ground must be connected, or you risk exceeding common mode voltage limits.
Also do note that RS422 is a standard for electrical interface only, it is not a communication protocol and thus transmitting bytes has nothing to do with RS422 itself.