Is it polite to answer a question asked by a senior by starting with "回...的話"?
starting a reply with 回 is too subservient in modern Chinese conversation. 

You only hear people use "回 + title" in period drama nowadays

In olden time, people would use  "回 + title" to replay to authority

e.g.  回皇上, 回大人

They didn't even normally talk like that to their father or teacher (they are in higher status and position, but they are also close to you, therefore, no need for subservient phrase like that)

回先生的話, 學生今年八歲 imply the student himself acknowledges he is not allowed to speak in front of the authority (in this case, the teacher) unless spoken to or with permission to speak. It is not the society generally think in modern time.