1. She will stay up late studying hard.

2. She will stay up till late studying hard.
3. She will stay up until late studying hard.
4. She will stay up late while studying hard.
5. She will stay up late while she study hard.
6. She will stay up late while she is studying hard.

[Which one can we use? aAe they all grammatical?]

1 and 4 are the best. 3 and 6 are just OK.

The others have errors in them.