If a woman is in her menses during the last 10 nights of Ramadhan, can she still hope for reward of Laylatul Qadr if she stays up during the nights and does all the worship allowed for menstruating women like doing duas, reciting prescribed duas found in the sunnah, acquiring religious knowledge, and so on?
Even if she doesn't stay up during the Qadr nights and doesn't worship at all, still she can hope to gain the mercy of Allah, let alone with all that worship:
قَالَ وَمَن يَقْنَطُ مِن رَّحْمَةِ رَبِّهِ إِلَّا الضَّالُّونَ
He said, "And who despairs of the mercy of his Lord except for those astray?"
Also note that menstruation is nothing other than harm and a discomfort for women:
وَيَسْأَلُونَكَ عَنِ الْمَحِيضِ ۖ قُلْ هُوَ أَذًى
And they ask you about menstruation. Say, "It is harm"
Allah (subhanuhu wa ta’ala—may He be Glorified and Exalted) says in surat al-Baqara, ayah 222, “They ask you concerning menstruation. Say that it is an adha (a harmful thing), therefore keep away from [your wives] during menses and do not have sexual intercourse with them until they have become pure [from menstrual blood], and when they have purified themselves [from menses by taking a shower (ghusl)] then you [husbands] may have sexual intercourse with them as Allah has ordained for you.”
(Al-Fiqh al-Islamiy, vol.1: 473) The Messenger of Allah (salla Allahu ‘alayhi wa sallem) told Fatema bint Abu Hubaish, “When your menses begins, leave off the salat, and when it has ended, wash the blood from your body and pray.” (narrated by ‘A’isha (radhy Allahu ‘anha—may Allah be pleased with her)
Quran is clear about menses. As far as a woman is concerned in her menses during the last 10 nights of Ramadhan, yes she still hope for reward of Laylatul Qadr if she stays up during the nights and does all the worship allowed for menstruating women like doing duas, reciting prescribed duas found in the sunnah, acquiring religious knowledge will be rewarded becuase the acts depend on intentions and good intentions are always rewarded and no injustice is made to any Muslim for act which Islam permits them to do Permisible actions during Menses will rightly b rewarded Inshallah.