If it is not vented, it definitely should be, for several reasons, one of which is how well it flushes. Also if it is rocking, then the wax ring is not sealing, which will cause it to leak sewer gas.
Sorry to be the bearer of bad news, but you'll need to fix the flange, or the wax ring won't seal. if you take a picture of the broken flange, perhaps we can suggest a repair method.
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