Firstly: 

It is obligatory for a woman to cover all of her body in front of non-mahram men, including the face. This is the correct opinion, as explained previously in the answer to question no. 11774. 

The woman is obliged to adhere to that even if she is in a non-Muslim society, out of obedience to her Lord and adherence to her religion. It does not matter if people stare or find it strange. Usually this astonishment fades after awhile, when the woman becomes known in her neighbourhood and the area around her. 

The fuqaha’ have stipulated that for it to be permissible for a Muslim to live in a non-Muslim country, the Muslim should be able to practice his religion openly. If he is not able to practice his religion openly, it is haraam for him to stay there and he is obliged to migrate if possible. 

For more information, please see the answer to question no. 146854 

Secondly: 

There is nothing wrong with wearing a jacket on cold days, on condition that it be worn under the khimaar. Thus the problem of showing the size of the shoulders and shape of the body will be avoided. If it is not possible to wear it beneath the khimaar, then the jacket should be large and not show the true size. 

Thirdly: 

It is permissible for a woman to work on her own in a place, if she is safe and can avoid being alone with non-mahram men, by leaving the door open or by having the front of the place made of glass, and so on; she should also limit conversation to what is necessary. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: I heard that it is permissible for a woman to work in buying and selling. Is that permissible if I adhere to hijab? 

He replied: Yes, it is permissible for a woman to work in buying and selling, or renting, on condition that this does not lead to anything that is forbidden in Islam and this is how it has always been among the Muslims. We see that in the case of ‘Aa’ishah the Mother of the Believers (may Allah be pleased with her): Bareerah came to her asking for help in freeing herself from slavery. Then ‘Aa’ishah bought her from her masters (and subsequently manumitted her). This is how people are nowadays: a woman may go to a store and buy something from the shopkeeper, and he may sell to her.  Similarly, a woman may have property that she rents out. The point is that there is nothing wrong with a woman buying and selling, but that is subject to the condition that it does not lead to anything that is forbidden in Islam. If it does lead to something that is forbidden in Islam, such as mixing with men in a haraam manner, then it is not permissible. 

End quote from Fataawa Noor ‘ala ad-Darb.

And Allah knows best.