You might want to consider replacing volume and squelch potentiometers with equivalent value digital potentiometers rather than coming up with a mechanical linkage. Reading the screen should be possible, but you'll have to reverse engineer what causes things to appear - there are a number of possibilities. If you know what the values are (for instance because your kepad just typed them), you can send those to the PC without having to read them.
This is probably not the first project you want to tackle. On the other hand, getting a keyboard matrix working and a couple of digital potentiometers changing values might not be too hard to start out with. Good luck!