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She will be up at night studying.
Should I understand the sentence above like
"She will be up studying at night." or
should I understand that like
"She will be up for night studying."
My guess is that 'studying' is a present participle and not a gerund.
You're right, "studying" is a participle there, not a noun. It's in the future continuous [ "will be" + present participle ].
"Night studying" isn't a compound noun here because "at night" is an adverbial of time, unconnected to "studying".
Your first re-written sentence has the same meaning as the original.
