If a menstruating woman stayed up all the night in the last ten odd number nights of Ramadan without praying but doing Dhikr and reading the Qur'an, is her Dua likely to get accepted?
Yes of course. Acceptance of every worship depends on the sincerity in the intention.
Menstruating female is allowed to perform all worship e.g. Thikr of Allah, Du'a, reading Quran (except the four verses of obligatory Sojood). She is not allowed to pray any Salah nor perform Tawaf around Ka'ba nor stay in Masjid.
Wassalam.