More than just prevention, can hydrogen peroxide soften and eventually get rid of plaque and tartar? Is it effective in whitening teeth?

No. Plaque and tartar that have calcified on your tooth must be removed by a hygienist. It may wear away slightly but won't go away completely. Yes, hydrogen peroxide is effective in whitening your teeth, however make sure you are using a professional product or one over the counter. Don't try and create something yourself, you will most likely damage your gums and or enamel.
No. Yes. No, hydrogen peroxide will not soften and get rid of plaque and tartar. Yes, it will whiten your teeth but is not the best t choice. Also it will kill some bacteria associated with periodontal disease but will not cure it.
No/yes. Hydrogen peroxide is deemed safe by american dental association to whiten teeth plaque can be removed by brushing teeth tartar needs to be removed by hygenist at your dental office.
No, kind of. Hydrogen peroxide will help kill bacteria in our mouths and bacteria is the reason we have plaque. Tartar or calculus is the hardened remnants of that same bacteria. So it will slow the growth of both. Yes, the rinse will also whiten your teeth very slowly. Few people can tolerate the full strength rinse so mixing hydrogen peroxide and water or any mouth rinse could be effective.