What is the definition of "kaft al-sha'r" (tucking up the hair) during prayer? Is it exclusive to men, or does it include women? And what should a woman do if her prayer garments are not suitable for unbound hair?

The prohibition of gathering hair in prayer — i.e., tying it up and collecting it — is a prohibition of disfavor (makruh), not a prohibition of unlawfulness (haram), and it is specific to men, not women. Thus, women are not included in this prohibition, and they may gather their hair in prayer in any circumstance.