Is it permissible to wipe over the head covering (paper or nylon) placed over henna, and is it necessary to wipe over all of it, or is wiping over part of it sufficient? Can this be compared to wiping over the turban? And what is the ruling on the prayer of one who does that?

It is permissible for both women and men to wipe over henna applied to the head during ablution (wudu') but not during ritual bathing (ghusl). This is because wiping over the head is based on the principle of ease and alleviation. The Prophet (peace be upon him) wiped over his turban and over his matted hair. Similarly, it is permissible to wipe over a plaster placed over the henna, and it suffices to wipe over most of the plaster. However, it is not permissible to intentionally place a plaster over the head for the purpose of wiping over it. Sheikh Ibn 'Uthaymeen mentioned the permissibility for a woman to wipe over her head covering (khimar) when there is hardship, likening it to a man's turban, and stated that it is permissible to wipe over a head matted with henna, gum, or honey. The purification of the head is alleviated by wiping, and this wiping is for minor impurity (hadath asghar) but not for major impurity (hadath akbar), with the exception of a splint (for a wound).