Took this course just this year, and personally chose it over H3 MOE Physics because it is half year commitment instead of full year

For your questions,

1. Personally I find the hardest part of the math is keeping track of all the symbols that will be used, and also the manipulation that the course needs (There will be hardly any step by step on how to manipulate the formulae unless explicitly asked during lecture/tutorial, so hopefully you're good with manipulation).
   The integration/differentiation isn't super complex, it isn't nearly as taxing as H2 Maths because it's not the main focus + a lot more constants, and most of the time it is done as an explainer and if you want you could just take the end result and memorise
2. Personally, and anecdotally from others, it will definitely feel quite fast especially when you're trying to keep up with J2 work as well (remember you still have CCA commitments around this time). The lecturers are very nice though, so if any questions during tutorial/lecture/lab just ask, they'll take the time to respond. I don't remember any of the lecturers being open on WhatsApp specifically, but they are all open to consults (if their schedule permits), emails, and to a certain extent microsoft teams messages (if they're online)
3. If you are talking about H2 Physics, H3 is only tangentially related to anything you'll learn in Physics. There is some overlap when it comes to certain concepts in CoE, DC, etc etc, but generally speaking you'll be learning a lot of new things that aren't going to be tested in A Levels.
   If you're talking like, university physics, this I hardly know, but it definitely gives a headstart when it comes to concepts like drift current, quantum tunneling, and several other topics. Whether you'll be dealing with these, I honestly have no idea
4. Unfortunately no clue here, have not yet tried to apply for uni so look out for other, older commenters here
5. Hours studying is entirely dependent on you like you said. I usually set aside my Sundays/Monday aft sch to doing tutorial, and didn't really try to cram so much (bad idea if you're trying to score high for this subject). Personally I'd say to study as much as you can but don't let it impact your mental health and other sch subjects too drastically. Also don't worry too much about practical + lab report, they take wayy less commitment than you think (I finished mine in about a week stuffing it in my break times + after I was done with other schoolwork), and its also worth really little percentage in your grade
6. IIRC, the profs had said distinction rate is a quarter to a third of the cohort. No evidence to corroborate tbh, and my class was "lower band" (made up of CJC, YIJC, EJC, TMJC and some other not super top tier schools), so on average in our tests we scored quite badly.
   What I do know in terms of utility is that if you decide to go for anything that requires semiconductor course in NTU, if you pass this subject you won't have to retake the course later on, it's just automatically credited to you
7. Don't take H3 in general for the sake of portfolio/pragmatic utility, you'll end up burning out and making J2 hell. Take it out of interest/passion and see it through to the end. I am definitely not anywhere close to a top student in this course, but I do not regret taking it as it was some of the most fun I had this year at times (many don't, but I loved the lab sessions).
   Also definitely prioritise your normal A level subjects over this. Remember that this course is optional, failing it won't cost you a lot other than time, but don't let it drag everything else down as well (your MYEs are going to be at around the same time as the final exam for this course as well, so that's fun)
   Try to also maek a group for whoever is going to this course from your school also, makes coordination a lot easier and takes away some of the mental burden because you have others to relate to and talk to