Does revealing the hair or wearing short-sleeved clothing at home in the presence of siblings’ relatives or colleagues, or shaking hands with men, nullify ablution?

Improper display (تبرج) is a grave evil that does not invalidate ablution (wudu’). It is permissible for a woman to show her hair and wear non-tight clothing in front of her mahrams (unmarriageable kin). However, shaking hands with non-mahram (definition) men is forbidden, as it is a means to indecency. As for ablution being invalidated by a man touching a woman, there is a difference of opinion, and the most correct view is that it does not invalidate ablution.