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

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ANSWER: No problem in this as long there is still time for isha.

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ANSWER: You should shorten your prayers in the hotel. In congregation, follow the Imam. You should not pray the Sunnah of dhuhr, Maghrib and isha as Prophet ﷺ used to skip these while traveling. Other than that, you can pray as many voluntary prayers as you want.

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