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Higher bond orders generally mean more stability, yes, and whatever you calculate to be your bond order generally seems to correspond to a type of bond (meaning, 0=no bond, 1=single bond, 2=double bond, 3=triple bond, though you can have bond orders of 1.5, 2.5, etc, so you can see why higher bond orders usually create more stable bonds, since they're stronger bonds).
Yes, I'm pretty sure that having a bond order that is fractional means that it has do something with a resonance structure. For example, Ozone would have a bond order of 1.5 meaning that it's the average of a double and a single bond.
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