Is it permissible to conceal good deeds such as fasting and prayer for fear of showing off (riyaa), such as answering "no" when someone asks, "Are you fasting?"

Concealing actions not commanded to be shown is legally مطلوب (desirable/required), especially if the doer fears ostentation (riya'). It is not permissible to intentionally lie by saying you are not fasting while you are, because the Prophet, peace and blessings be upon him, said: "Indeed, truthfulness leads to righteousness, and righteousness leads to Paradise. And a man continues to be truthful until he is recorded with Allah as a truthful person. And indeed, lying leads to wickedness, and wickedness leads to the Hellfire. And a man continues to lie until he is recorded with Allah as a liar." Instead, you can use equivocation (ta'ridh) by employing a truthful phrase that the questioner understands to mean the opposite of reality, for "equivocations are a way out of lying."