what water clarifier does is bind to particles suspended in the water and causes them to be large enough to sink or get caught in the filter.
it does not react with carbon and is perfectly safe. however, depending on the amount, you can see it collect and make a film on your filters media.
you can rinse the filter in the bucket when you do the partial water change is fine. however, do not rinse the filters in the main tank or you would just be putting the little particles back in.
rinsing a filter under tap water for 10seconds does not cause the bacteria to explode on contact. like I said, dont go soaking your filters in chlorinated water, but rinsing them off and putting them back in the tank is the most practical method.
now, you do not have to use water clarifier, but it may take days for your water to clear instead of hours.
in the case of soaking the wood, yes you want to use tap water for the first soak or two. you want everything to die that might be alive. This is all just my opinion.