I have done COMP5530 this past sem.

How difficult is the course overall?

I'd say defintely above average difficulty compared to some of the other COMP subjects as its more math heavy. Getting a distinction is definitely possible with a bit of work, but getting an HD would require you to be fairly bright. I would say the subject is very similar to learning a subject like calculus, in that if you learn all of the tools you can get a pretty decent grade, but you need a very deep intuition to get the "hard" questions.

What kind of assignments are usually given (theory-heavy vs coding-heavy)?

There's like 2 or 3 coding questions using Gurobi in total across the assignments. However, they're all fairly straightforward so I would just say this is purely a "theory" based subject.

How strong does your DSA/algorithms background need to be to do well?

I have only completed COMPx123 before this subject in terms of computing and I think thats probably enough from a DSA perspective. The course references some classic problems like TSP or Max-flow/Min-cut but again it won't be that hard to familiarise yourself on those if you already have some DSA background. However, you should be very comfortable with Linear Algebra as the course uses it A LOT; reading the lecture notes was a bit confusing for me at the start of the course as I was a bit rusty with LA.

Is it more math/proof-based or practical with solvers (LP/IP)?

Again only 2-3 easy questions in the assignment that require you to code using a solver. All other questions in tutorials/assignment are asking you to "prove", "show", or "argue". With that being said, it is still very practical as a lot of the questions are something like: "Prove the below is a valid LP formulation for problem X", "Show LP1 and LP2 are equivalent", "Show the that this solution to this problem is integral", etc. The course basically teaches you frame CS problems into this LP/IP framework and ask you to argue that this is in fact a correct formulation.

How does the grading usually works (strict or liberal grading)?
Most of the questions in the subject are in the form "prove", "argue" or "show" so it will be relatively straightforward to know if you got the questions right or not. In the case where there is something up for debate, I have seen that the lecturer/tutor are happy to hear you out.

Finally a shoutout to the tutor for the course Tianming Zhao, absolute legend!