ANSWER:

No problem in making dua after tahajjud as the Duaa in the last third of the night is accepted. 

She should not do this after other prayers.

https://youtu.be/hYToZVeAl20

My friend makes dua cuping hands after tahajjud salah and any other salah except fard. Is it allowed?

Prayer, Taraweeh, Tahajjud and Qiyam-ul-Layl | May 25, 2019 4:03 am
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Its has been a habit for me to pray night prayers from the 1st day of Ramadan to the last day from 4:30am to 5am. So I normally skip witr during the prayer in the mosque so as to pray it after my night prayers. Am I doing the right thing skipping witr? Can I pray the witr with the immam and also repeat it after my night prayers?

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Some of women in our country wear maxi(long dress upto feet) .They ask me wheather their prayers will be valid if they don’t wear under garments,that is from below private parts uncovered.