What is the ruling on a girl taking private lessons in her friend's house from a young male teacher, with the friend's family present in the house but not in the same room, knowing that both girls wear the hijab and do not cover their faces or hands, and that mixed-gender interaction is common in their society? And is this considered khalwa (unlawful seclusion) if there are two female students?

The first preference is for a woman to conduct the study to prevent fitna (temptation/strife) and suspicion. If no woman is available, then it is permissible for a young man to conduct it, provided that fitna is assuredly absent. Khalwa (definition) (impermissible seclusion) is negated by the presence of two trustworthy women, or if the place is accessible to others, as mentioned by the jurists.