I'm very late to the party, but I'll contribute a little. I study B. Science (Adv Maths) at USYD, majoring in mathematics and statistics, minoring in IT/comp sci. (I also used to study economics, but nevermind that.)

As far as I know, I should be able to meet most of prerequisites of the courses due to my subjects (though, I'm concerned if 3U math alone will suffice as it seems some uni courses recommend 4U maths to be taken.)

This is not much of an issue as first year maths courses runs through whatever you need in 4U. But if you have the time after HSC, I recommend reading up on 4U complex numbers and integration on your own.

1) What are the employment prospects for graduates with commerce/computer science and commerce/math degrees?

With commerce and maths, the obvious route is going into quantative finance or data analysis for financial institutions, both of which are very popular along my friends who only study (pure/applied) maths (without commerce). People who only major in statistics often go for the latter. Consulting is also a path for mathematicians and statisticians.

For computer science, the above route is also possible, as trading companies have technical teams dedicated to software (in constrast to maths majors who usually join as traders). Software engineering, technical support and data management for big companies is also very viable.

2) What is the difference between software engineering and computer science? Would commerce/software engineering be a viable combination as well?

There is significant overlap between software engineering and computer science, e.g. in both disciplines you're expected to learn how to code in various languages, abstract data structures, algorithm design and analysis, et cetera. However, half of software engineering is dedicated to studying project management and design paradigms, while computer science courses will focus more on the abstract and mathematical theories (e.g. turing machines, programming language theory, et cetera).

For this reason, if you enjoy maths and engaging in abstract ideas, you should go for computer science and not software engineering. I have many friends who transferred from software engineering to computer science (under B. Sci), but I don't personally know anyone who go the other way around.

3) For those who are studying computer science in university, what is it like exactly? I do have an interest in programming and tried it multiple times in the past (I did find it enjoying actually!), but I'm unsure whether programming is best suited as a hobby rather than something I fully study as a course, if that makes sense.

It's hard to describe all of computer science units as a whole, since they can be very different (e.g. studying algorithm design/analysis vs programming languages). However, generally, you go to your lectures where the lecturer goes over theoretical and practical concepts, and each week you have a problem set you have to work through during your tutorial classes. Various take-home assignments take place during the semester, in which you are given a practical problem, design and describe your solution, program it and pass given test cases, and analysis your solution.

I took a senior algorithm design course last semester. Typically in a lecture, the lecturer would describe a practical scenario which motivates a (often mathematical) problem, which leads into design paradigms which produce algorithms which solve the problem.

4) Supposedly I do choose computer science, which universities offer the best computer sciences courses after UNSW and USYD? I don't think I will make the ATAR cutoffs for both especially coming from a mid 300s ranked school, so I want to consider other universities as well, like maybe UTS or Macquarie.

Off the top of my head, I think UTS is a decent university to go to for computer science. I know someone personally who started off in UNSW comp sci, then transferred to Macquarie comp sci, but this is unusual.

However, I would still love to learn a bit of programming during university, which I'm thinking of learning through maybe subjects involving programming or even minors? I considered learning programming in my own time as well but I'm not sure if I would even have enough time for that. How would one go about learning programming without taking an entire degree on computer science/IT/software? Still need to do quite a bit of research, but my first preference will be UNSW since I figured there's really no harm in trying out.

If you have electives, spending them on comp sci is a very good idea, especially since you're studying maths/stats. This should lead you into studying programming/comp sci on your own. Moreover, if you can do a minor in comp sci alongside your other majors, then I would definitely recommend it.

Studying programming on your own from scratch is also very doable. I think you have some programming experience, so that's a good start. There are plenty of websites to learn coding, and youtube videos which can go into more abstract topics in comp sci (e.g. algorithm design paradigms). Moreover, it's very easy to google computer science course notes of various univerities online, or even entire textbooks. But this is subject to your time constraints.

In case I still don't make the cut-offs to UNSW or USYD, how are UTS and Macquarie in terms of their math facilities?

Macquarie is a leading university for actuarial studies, which should mean that it has a decent applied mathematics/statistics faculty. The type of mathematics taught to actuarial students are similar and often coincide with financial mathematics, so I'm sure they teach it decently.

I hope this helps, and good luck!