holy smokes you ask a lot of questions- you realise that's why they had the info sessions, congratulatory evenings, HR information nights, etc... right??! I hope everything works out for you because based on the questions you're asking, I wouldn't offer you a traineeship purely on your lack of understanding of what you are signing up for.
In short, back when I did it I was doing night classes which were dependent on subject. Nowadays they still offer evening classes (only on weekdays) with lectures from 6-8pm but a lot of employers are flexible and will let you move time around or take leave/skip lunch breaks/etc so that you can attend your lectures and tutorial (another hour on top of the lecture). If you have the choice, make sure you enrol and select classes/timetable asap at respective university so you can balance your workload. Work hours depend on firm/division- some people do 8:30-5:30 their whole life, whilst others can do 9-9, or 9-12 (yes that's midnight).
I originally joined audit and worked on clients all over the place which was a bit of a hassle since I was never in the city which made getting to uni a bit harder- being able to drive was very helpful. I later transferred to Financial Services so I was always based in the city which made uni a lot easier. Depending on client/engagement, you can go with your team, sometimes the senior will drive, sometimes you all catch a taxi (or whatever is most practical/efficient). Balancing work commitments and deadlines with university is always a challenge but the tip is to ensure that everyone is aware of your commitments as early as possible- i.e. don't just tell your senior on the day before an exam that you need to go for an exam, tell them a week in advance so they know to expect you won't be able to stay back/etc.
Moving up in terms of promotions is based on performance, and the performance criteria includes a time-based/experience-based criteria (e.g. 2 years). Usually each year you will get some kind of pay rise for both inflation and general expectation that you have become more competent/independent in your work without requiring as much hand-holding. Don't expect too much- maybe a couple of $k. That being said, my friends in mid-tier firms at the time were being paid about $38k p/a compared to my $33k p/a in my 2nd year.