子供の頃 と 子供の時 はどう違いますか？説明が難しい場合は、例文を教えて下さい。

In many cases, they can be used interchangeably, but since 「～の頃」can express a range of time, I think it is more likely to be used when referring to the actions that you used to do or continuous situations in the past.

例）わたしは子どもの頃、友だちとよく外で遊んだ。

And when we say "When I was a kid", we don't indicate when exactly it is, so I feel 「こどもの頃」might be more commonly used than 「子どもの時」. As for 「高校生」, it is rather specific, so both 「高校生の時」and「高校生の頃」sounds natural to me.