Hi!
こんにちは!
Regarding 頃(ころ) and 時(とき), the general idea is that "toki" is a simple pointer to time while "koro" refers to a general timeframe.
1. 子どものとき、僕は母に本を読んでもらいました。
In this case, you are referring simply to the time when you were a child.
2. 子どもの
ころ、僕は母に本を読んでもらいました。
This refers to a span of time, i.e., your childhood.
3. いつ頃つきますか。
Similarly, this asks the general timeframe (that is, the approximate time). The question suggests the speaker is asking only for the approximate time and not any specific time.