To answer the first part of your question... whitening toothpaste is infused with a mild peroxide solution... usually about 3%. It might even help a little except it quickly becomes diluted with saliva and doesn't stay in the mouth in contact with the teeth nearly long enough.
The same peroxide is used in many of the whitening "strips" and some of them actually provide a noticeable lightning of the front teeth, but the strips stay attached for several minutes each time... as does your dentist's treatment.
There was a frenzy of whitening teeth in Europe and England during Victorian times, but unfortunately they used common bleach... did a fine job but destroyed the tooth enamel and the users went to their graves with terrible ttoth problems such as abcesses.... Ah! vanity!