If you are wondering what is the different between a law research assignment, a problem question assignment or a case analysis assignment, you might like to look at Chapter 5 'Academic Legal Writing' of Nichola Corbett-Jarvis, Effective Legal Writing : A Practical Guide (LexisNexis, 3rd ed, 2020).
If you want a quick overview of legal grammar, you will find Chapter 3 'Effective Legal Writing' in Michael Meehan and Graham Tullock, Grammar for Lawyers (LexisNexis, 3rd ed, 2013) useful. It is available as Reading 6 'Effective Legal Writing' in Daniel Goldsworthy & Michelle Bendall (eds), Research and Statutory Interpretation (LexisNexis, 2021).
The Academic Phrasebank produced by The University of Manchester is a useful generic guide on academic writing skills. Sections include: