1) What is the best order to study the topics in? My school sadly is sometimes known for having a dodgy way of ordering topics so that we have very little time to work on harder and more in-depth topics as they are placed unnecessarily close to trials.
The syllabus does have the topics put in an order, and this is generally a good way to follow the course. People typically start with either Graphs or Complex Numbers because they are the 'easiest' to grasp and in the case of complex numbers, provide something new and (hopefully) exciting. Some topics flow on from others (such as Volumes flowing on from Integration.) However, if you follow the syllabus, you should be fine.
Also, the syllabus does say that "... approximately 30% of time should be devoted to Harder 3 Unit Topics." The only way to really learn this topic is to do past papers, as they can throw in anything from 3 Unit in there and make it a lot harder. This is the topic that gets a lot of people, so you should definitely devote a fair bit of time to feel comfortable with it.
2) Aiming for an ATAR above 99, what would be the ideal time for me to learn all the topics by? I have done accelerated maths for 2U and 3U, so I will have much more time to practice and learn 4U maths, and I also prefer learning topics before my school teaches them. Our trials are around August.
Before the HSC exam starts would be a pretty good time. Alright, fine: I'll be serious. A lot of the time, the course isn't completed by the trials. For me personally, there was still a bit of mechanics and all of Harder 3 Unit to study after the trials. I finished the course about two weeks before the final day of school.
Your school may vary, but as long as you keep up with the class, you'll be fine. If you haven't studied topics by the trials, then they will remove the questions (and give replacement ones if there is a substantial amount missing).
3) I've heard that speed is everything for the 4U maths exam. How should I teach myself pace, and how do I push myself to do questions with lots of speed (+ accuracy lol)?
The best thing to do is learn a lot of the tricks with how to answer questions. For example, if you encounter a polynomial and find a factor, it is a lot easier to do a division "by inspection" rather than going through the whole long division process. Learning things like this will save you time, which does matter a lot in the 4U exam.
You also could get a calculator like the "CASIO fx-100AU PLUS." This calculation is on the list of approved calculators, and can do complex number calculations. This is a huge time saver (you can check you work in longer responses, and very quickly knock out complex number questions). You should also learn how to use all the features of your calculator, such as the memory.
Another thing to do is prioritise questions. Some questions, such as 15(b) in the 2018 paper, take a lot of time to do and give you very little marks comparatively. If you skip this question until you've attempted all the other questions, than you can maximise the marks you get for your time. Of course, you have to be careful with this. Don't use all the extra time you gain staring at harder questions, as that question is still a fairly easy 5 marks.
In regards to textbooks, I don't know much (I only used the one throughout the year), but a very helpful resource is Eddie Woo's YouTube channel. He is an amazing teacher, and can easily explain any topic in the course. It's great to watch his videos if you're struggling with the textbook and/or your teacher.
1) Which schools have the best past papers?
I find that NESA makes some pretty good past papers. Alright, fine: no more jokes. But, seriously: you should definitely try the past actually HSC papers from 2001 onwards. A website called "thsconline" has an extensive catalogue of past trial papers, and answers to past HSC papers that NESA didn't give solutions to. You should see if you can get any past papers from your school (ask your teacher for some), as they'll best prepare you for the internal assessments. Your school should also have copies of some of the more widely used papers, such as the CSSA and Independent papers. Other than that, it shouldn't make a difference which one you pick. If they made it online, then they are obviously worth something to some people. So pick one that looks interesting, and have a go at it.
2) Should you integrate these past paper questions as you learn new topics or should you finish all textbook questions then move on to just doing past papers?
I think that you should start looking at them once your first assessment task is coming up. You could also look at them after you finished a topic, but not during it, as you have no way of knowing if it's a question which requires something taught later in the topic. Also, if you do study them throughout the year, it's pretty satisfying being able to do more and more of the paper (and eventually complete it).
I hope this helps. Good luck with the year ahead of you.
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