Answer
(Fatwa: 797/667/B=1432)
(1) If one does not wear topi due to humility, humbleness and meekness then salah shall be lawful without being makrooh. But if one offered salah bareheaded due to carelessness and fashion, then it is against etiquette and makrooh, he will receive less rewards.
(2) One can offer salah in T-shirt or half shirt, the salah shall be valid but it shall be makrooh if the elbows are open. One should offer salah in the dress of pious persons.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband