Seeing as how I'm only allowed to use one Z-move per battle, I haven't had much experience with them. However, I've noticed that I've never missed a Z-move. Are all Z-moves guaranteed to hit? Does the accuracy of the base move influence it and I've just been lucky all this time?
Damaging Z-Moves don't make accuracy checks
Similar to moves such as Swift, all damaging Z-Moves skip the accuracy check, meaning they not only have 100% accuracy, but also ignore changes to the user's Accuracy stat and the target's Evasion stat. Furthermore, Z-Moves can even hit a target through Protect and similar moves, though they only deal 1/4 their usual damage in that case.
Status Z-Moves simply add an extra effect to the normal move, rather than creating an entirely new move. It sounds like the extra effect from being a Z-Move applies before the normal effects of the move, so they presumably always work, but the normal effects of the move would still be subject to accuracy if the original move was (e.g. Z-Toxic would always give +1 stage Defense, but might fail to badly poison the target).