How does a person adjust the short pin that sticks out of the front of the cueing frame? Is this just a matter of putting a bit of pressure on this to force it down relative to the arm cueing support bar?
Yes, it swivels down or up as required, pretty easily. A fingertip will do.
(I assume that one should make this adjustment with the cueing lever down so as not to put too much pressure on the hydraulics of the arm lift cylinder.)
Yes, though the main reason is that it's safer for your cartridge to do this with the arm locked down.
The silicone fluid in the lift cylinder is not part of a hydraulic system in the sense you're probably thinking (and as I once thought). It's just a lubricant. Cueing speed is controlled by the white nylon screw, not by the fluid.
Nothing you're likely to do will put that fluid under any pressure. Excessive pressures on the cueing mechanism (like raising the cueing lever with the arm locked down) could bend some of the parts. It's unlikely to cause a fluid leak.