He needs to do some basic geometry. The two thrusters are not directly opposite, they are separated by the spacecraft.
Wow, and how. That's basic spacecraft dynamic control. In the real world RCS thrusters are never optimally placed, so we always design according to a generalized free-body method. Even though the quads are ostensibly placed to give "pure" pitch, yaw, and roll moments, that is never actually achieved in practice. So any "pure" maneuver in the cardinal axes always requires multiple firings from RCS jets you wouldn't think are appropriate to that. One of the hardest things to do in manual spaceflight is "nulling" or trimming after a burn, to take down the residual unwanted rotations in odd axes.
Fun fact: the reference axes for the LM RCS were
not an orthonormal basis like you'd expect. It was biased for forward motion, to optimize the control solution for landing. There's a great paper out of MIT's Draper lab that explains and justifies this, and it has a good introduction to basic dynamic control theory. The generalized free-body method is explained in full in Sidi's book, which is still the standard reference.
As for modulated signals, that's almost a no-brainer. You often get the carrier for free from the power supplies, and a passive band-pass filter can be made for a few bucks using a home electronics kit. Not only is it much, much safer in the space environment, where you can have transient electrical and magnetic interference and short circuits, but it also lets you multiplex different control signals on the same wire. That way you have to run only one wire out to the RCS from the controller, and then split the different signals out at the remote site. It saves mass and electricity.
