How does the geometry of cross bikes affect on-road handling?
A lot of people commute on cross bikes just fine (and even prefer them to conventional road bikes). He's full of it - the amount you'd need to forget to have issues is roughly being confused enough to think you're an onion (and if you're this confused, well, you're screwed anyway!), especially at commuting speeds. There are different bicycles for different purposes - for example, you're not going to take a touring bike like the Trek 520 and compare it to a racy road bike like the Specialized Allez. You probably wouldn't want to enter a road race with a cross bike, but commuting is a fine purpose for a lot of them. 

There are 2 sorts of cross bikes - ones meant for racing , and ones meant for regular use (e.g. Trek Crossrip). These aren't necessarily disjoint (e.g. Kona Jake the Snake is used for both, to some extent), but you can tell roughly what they are for by looking at the components spec'd (example description for the Trek crossrip). 

Obviously, you want slick tires for your commuter (if you're on the road) since the slightly knobby cross tires that come with them increase noise and can lower cornering speeds (For example, cornering quickly with a mountain bike on knobby tires does lead to washouts sometimes due to the knobs squirming). But things like the Kenda Small Block Eight are fine for commuting. 

Typically, cross bikes have higher bottom brackets, larger tire clearances, cantilever/disc brakes, longer wheelbases , cables routed so that you can shoulder the bike easily and more relaxed geometries than road racers. This serves to give more shock absorbance and stability for the bike. The more commuter oriented variants also have easy fender mounting, rack mounts, etc. 

I think the other parts of your question are answered in your related questions and the Wikipedia article. 

Not really an answer to the question: Since rain, snow and grit do tend to damage drivetrain, you may just want to use an old cheap rigid mountain bike (e.g. 80s-90s Specialized Hardrock/Rockhopper, etc.). Great tire clearance, very stable, cheap to replace parts on, discrete (so they don't attract attention in the bike rack), etc.