How can a woman perform ablution while wearing her hijab in the street or in exposed places? Is it permissible for her to perform tayammum in this situation? What should she do if she cannot find dust for tayammum?

It is unlikely that there is no place where a woman can perform ablution away from the sight of men, especially in Muslim countries. Even in non-Muslim countries, there are public restrooms. If it is assumed that ablution is impossible except by exposing her 'awrah to men, then she should perform tayammum. It is also unlikely that there is nothing with which to perform tayammum. If it is assumed that there is nothing, then she should pray the prayer of one who has lost both means of purification.