I would like to have some explanations on why Uthman RA decided to not marry Hafsa RA. What elements made him decide not to. I have read a few posts about the story but none of them has an explanation on Uthman decision.
Actually 'Uthman () never planed to marry Hafsa (). Even if both became widower and widow.
All we know from history is that at the end of the I'dah after the death of her earlier husband (Khunais ibn Hudaifah) her father 'Umar asked his friend and companion abu Bakr whether he wanted to marry his daughter, but abu Bakr rejected politely. Then he moved asking his next friend 'Uthman, still hoping to find an appropriate husband for his daughter. But 'Uthman was hoping to marry his former wives sister Umm Kalthoom as he just became widower after the death of Ruqayyah (daugther of the prophet ()).
After both rejections 'Umar went disappointed to the prophet () complaining and the latter told him both 'Uthman will get a better wife than Hafsa and Hafsa will get a bettere husband than 'Uthman.
As soon as Hafsah had completed her waiting period, her father Umar offered her hand to Uthman Ibn 'Affan, and thereafter to Abu Bakr; but they both refused her. When Umar went to Muhammad to complain about this, Muhammad replied, "Allah will marry Uthman to better than your daughter and will marry your daughter to better than Uthman. (source: wikipedia/ibn Sa'ad)