Question: When offering Salah is it permissible to wear T Shirts? I have seen some people at my mosque do this and also some brothers do not wear a hat when offering salah.
Answer: It is allowed to pray in a t-shirt. What is makruuh is to pray with a bear upper body, without anything over the shoulders. It is makruuh to pray without a hat unless one does so out of humility.
... and Allah knows best.