Is it permissible to manipulate words instead of lying, such as when a person says "yes" with the intention that he ate yesterday, when asked if he ate today and he did not?

If a person needs to withhold the truth about a matter, they can use ma'areedh (euphemisms/allusions) for tawriya (equivocation), which is to speak words intending something other than what the listener understands. It is established from the Companions, such as Umar and Imran ibn Husayn, that ma'areedh provide an exemption from lying. Imam al-Bukhari dedicated a chapter titled "Ma'areedh are an exemption from lying." So there is no harm in equivocating with words that make the listener understand something other than the truth.