Is determining a specific number daily for adhkar and prayers upon the Prophet (peace be upon him) and maintaining that, and teaching others to do so, considered a bid‘ah (innovation)?

There is no harm in maintaining a specific number of remembrances (dhikr), prayers upon the Prophet, or seeking forgiveness. However, one should not claim that this is a prescribed Sunnah for everyone, or believe that there is a special virtue in consistently doing so, as there are many indications from the predecessors supporting this. There is no objection to telling your family or brother about some of this, but it is better to keep your good deeds private. So you might say: "Maintain tasbeeh (glorification of Allah), for some people regularly recite it a hundred, or a thousand times, or so on," without mentioning your own practice. Whoever is able to have a hidden good deed, let him do so.