My timetable is pretty similar on Mondays and Tuesdays, but consisting almost of back-to-back lessons. I don't get a lunch break on Mondays, so I'll have to somehow take something I can eat on the move, most likely a (chicken) salad wrap as they are super quick to make (I know you're vegetarian, so ignore the chicken!) and obviously portable. Snack-wise there's always Special K bars or something similar.
I'm only planning to take my core reading folded up in my bag and my laptop - I use my laptop for everything, as it just makes things so much easier, especially as I have a 2 hour commute and don't fancy lugging heavy bag about. I just had a handbag in first year and it worked perfectly -it was big enough to fit things, so not one of those tiny little bags that you can just about fit a penny into! In the bag I'll have for next year, I'll carry a slim laptop, keys, phone, water/small food box, and maybe a pen or two in case I fancy making notes by hand (which hardly ever happens, but still).
Gym-wise, you're going to be running around a lot as it is by the sounds of things, so just slot the gym into the weekend. Don't add any more stress to your longest days in university, as you'll end up knackered and fed up with everything, and probably won't have enough energy to even make the gym anyway!
Really think about your bag, though. I know bags that can fit everything into are handy for carrying more about, but it also means you're carrying a bag that weighs more. If you buy a smaller bag that forces you to carry less, then you learn to prioritise (for example, I no longer carry my make up bag and about a gazillion hairbrushes any more, because I can't fit them!)
Hope this helps!