Divorced woman working

My wife's sister's daughter is a divorcee. She has decided to move out from her parents home to live in her own accommodation in another city on the basis that the existing commute to work is too long.

She claims her father is unable to support her financially due to his age & alleged irregular income. She has no male siblings but does have uncles (mahrams). However culturally it is considered below one's dignity to seek financial support from one's uncles. She claims that her case falls within the remit of dharoorah (necessity)

1. Would the concept of dharoorah apply in this situation? Surely if the situation is, as she describes, then she could do jobs from home and place tawwakul on Allah. The little income will be sufficient.

2. The fact that culturally it is considered below one's dignity to seek financial assistance from one's uncles does not necessarily mean that they collectively or individually would refuse to assist. If it were explained to them that they need to save their niece's imaan, surely they would understand.

3. It is only the essential needs of the divorcee that need to be fulfilled, i.e. clothing, food and shelter which is currently being catered for by her parents as has been the case since her divorce.

She will be going to work without niqab & in an environment of free mixing. Questions:

a. Based on 1 - 2 above, is it correct for this lady to abandon the explicit command of the Qur'an which instructs women not to emerge from the home, i.e. would hers be an exceptional case based on necessity?

b. If it does fall within the category of necessity, is there a need for her to work at a place that is far from her home in a mixed environment without niqab?

c. If the answer to a or b above is "no", is this lady's income halal or not?