Idiom Request – Idioms Similar to ‘Some Things Are Better Left Unsaid’

Your first example, where the sentence is technically true but conveys a false meaning, would be considered sophistry in English. Informally, we might call these weasel words or, in some situations, use the recently coined word truthiness.

If you tell the truth about something, but hold something back, as in your second example, you could call that a half-truth. If you say, "I can't be drunk, I only had one beer," but you also drank a bottle of vodka, that would be a half-truth. This seems closer to your second example.

However, in my experience, most English speakers would be more likely to describe these situations in more general terms, as a trick, than to use a term specific to this sort of language.

You can go cap in hand to someone, if you're humbly asking them for something.