ANSWER:

If there are no non mahram around, no need to cover herself up with hijab while doing anything. 

Hijab is not a requirement for dua or wudhu.

Is it ok to wear hijab for a woman while performing wudu at home or when she is in dua? Is she obliged to do so? Did prophet Muhammad ﷺ recommended it? Please clarify the Sunna of wearing hijab at these times for women.

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