Is working remotely, with electronic communication with a team that includes men, considered unlawful mixing (ikhtilat)? And is her current work, which aims to provide funds for her parents' Hajj, unlawful (haram) given the presence of mixing?

The husband is obligated to fulfill the condition of allowing his wife to work during the aforementioned period, as the condition is not forbidden as long as the woman works according to legitimate regulations. The husband has the right to prevent his wife from working in a mixed environment based on his guardianship. If she is able to work remotely, there is no harm in that, provided she adheres to not speaking with men except within the limits of necessity and work requirements. The wife is not obligated to work to provide for her Hajj expenses or for her parents, but if she does, it would be an act of righteousness.