Is it permissible for the husband's brother to enter the house in the husband's absence? And is the mother or sister a Mahram? And is it permissible to go out or sit with the sister and her husband? And what are the conditions for Mahramiyyah?

It is permissible for your sister's husband to enter the marital home with his wife if the husband gives permission or his consent is known, provided that there is no forbidden khalwa (private seclusion) and that fitna (temptation/discord) is safeguarded against, along with adherence to full hijab in his presence. It should be noted that the mother and sister are not mahrams for a man during travel; the mahram referred to for travel is a mature, sane male. It is permissible for a man to sit among a group of women, some of whom are his mahrams or wives, if fitna is safeguarded against, he adheres to lowering his gaze, avoids softness in speech, maintains the covering of awrah (intimate parts), and they only speak to him when necessary.