I think there are not so much differences between 誉める and 褒める. I give you some examples. その親は学業成績で子供たちを褒めた。: The parents praised their children for their academic performance. 授賞式の参列者は彼の偉業を誉めたたえた。: The attendance at the awards ceremony admired him for his great achievement. 量る：We use 量る when we measure the weight of something. 計る：We use 計る when we measure a number or time.

A) 誉める and 褒める After looked up the dictionary, i think it's the same. But people usually use the latter one. B) 〔計る〕：時間・数量。Time, quantity. 〔量る〕：重さ・分量・体積・容積。weight, amount, volume, capacity.