It looks like I have one key with right groove and one with left grooves. Is that normal?

No. A ZX should have a single key that fits all locks. Sounds like one or more of your locks has been replaced.

Ok...my ignition was probably replaced at some point. It's on a different key than the door and hatch locks. I haven't tried the glove compartment and body side pocket lock, but I'm guessing I won't be able to lock them, since they're on the master key. Oh well, that's not too big of a deal I guess. Thanks!