On second thought: (表示已改变想法)又一想,转念一想

e.g. I'll wait here. No, on second thought, I'll come with you. 我就在这儿等.不,再一想,我还是跟你一起走.

3. I thought after the whole arrest scandal, out of sight, out of mind.
我以为逮捕丑闻过后这么久该平息了.

out of sight, out of mind: used to say somebody will quickly be forgotten when they are no longer with you 眼不见,心不想

4. But the little white lies that I tell my family are none of your business.
但我向我家人撒些善意的谎言与你无关.

white lie是指为避免伤害他人感情的时所说的善意的谎言,小谎 harmless or small lie, especially one that you tell to avoid hurting somebody

"撒个小谎"就可以说成"to tell a white lie".

e.g. When she asked me if I liked her dress I had to tell a white lie. I thought it looked awful, but I couldn't say no! 当她问我喜不喜欢她的新装时,我只能撒个小谎.其实我觉得那件衣服难看之极,却不好直说.