How to study better when underprepared for grad level theory course
It's great that you have a study partner.  What you could add is some regular visits to office hours (TA and instructor if there are both).

As for sacrificing research work at crunch times, this is something you should discuss with your research supervisor.

Edit (responding to comment)

Thoughts about how to benefit from visiting office hours:


Go over portions of the lecture notes you're not solid about.
You may have some gaps in your background knowledge and skills, which you can work on with one-on-one guidance.
You can bring a draft of your homework:


Check your reasoning.  Your instructor or TA can point out places where you make a leap of faith in a proof, where you could consolidate some steps, or ask if you've considered such-and-so other approach, e.g. indirect proof.
Get unstuck on a problem.
Better understand the relationship between an example worked in class and the problem posed in the homework.

Get additional practice with certain key types of problems.
Learn tricks for working more quickly -- which can be extremely valuable in an exam setting.
Practice explaining a topic.  At a key juncture your instructor/TA can ask you to be more precise if necessary.  Getting feedback about which of your ideas are correct and well put in itself can help you gain more confidence.
Request a practice exam, and have it evaluated.


In short, in office hours you can receive tutoring at the source!  (Always being sensitive to the instructor's or TA's need to balance your needs with those of the other students.)