Is a girl obligated to wear the hijab, or is the male mahram obligated to lower his gaze to avoid temptation between unmarriageable kin?

The basic rule is that it is permissible for a woman to be alone with her mahrams (unmarriageable kin), and it is permissible for a mahram to look at what is ordinarily visible of his mahram’s body. However, if fitna (temptation/strife) is feared, then it is obligatory to block the means leading to the forbidden. Thus, a man must avoid being alone with or looking at his mahrams with lust, because this is forbidden by scholarly consensus. Similarly, a woman must abandon what leads to the forbidden if she fears fitna from some of her mahrams.