I did an exchange semester in Singapore, and really it's not that much more expensive here, apart from the insanely low prices for meals in S'pore. Some general points:
Goods are about the same price in CHF as they are in SGD. So overall it's about 30% more expensive here.
Electronics and imported stuff is often cheaper here (and no I'm not talking about the rip-offs at Sim Lim, I'm comparing with the actually cheapest prices there). This was a bit unexpected. Summer clothes are more expensive here, but if you are looking to buy a winter jacket or anything that is not everyday wear in Singapore you sometimes actually get better deals here, or even better in Germany. There are huge discounts at the beginning and end of the seasons, and especially Germany is dirt-cheap for clothes.
Rooms in shared flats in central Zurich are 400-700.-/month. It's much cheaper around ZHAW/Wintherthur however, but I don't have numbers as I live in central Zurich. Flats/rooms in Switzerland are significantly larger than average flats in Singapore, so you should have enough space. (Usual rooms are around 15-20 sqm).
Services are much more expensive. Haircuts, someone cooking food for you, getting pants shortened, etc. is all much more expensive here. A lot of businesses have discounts for students so that lessens the blow somewhat.
Food: An actual meal at ZHAW dining halls ("mensa" in German) costs around ~6.- which is cheap. Most people just buy food at the store and cook something themselves, it's really not hard to cook rice or pasta. Local vegetables are often cheaper than in Singapore, meat is more expensive. The base cost of a self-cooked meal is around 1.- to 2.- for pasta or rice with sauce, but with meat that can go up to 5.- to 10.-. However: A lot of the cheap meals I had in S'pore actually didn't have a whole lot of meat on them, and portions were a lot smaller than what we are used to here. So I don't think you should worry too much about the food: As long as you don't go out to eat (and nobody does around here), you'll be fine.
Buying food in Germany is not cost effective if you don't have a family to feed and don't have a car. There are several of the cheaper grocery stores (Denner, Lidl, Aldi) here that sell lower quality food (e.g. no name brands and imported meat from the EU) that is a lot cheaper and totally fine. The only reason to go shopping in Germany is for clothes: There prices are about half of what clothes cost here.
So as for your actual questions:
2.a) Train travel: Get a half-price card (175.-/1yr) immediately. You get ~50% off of all single tickets or day passes on trains/buses/trams. It will pay for itself even with only 2 or 3 longer trips. If you are under 25, you can additionally get the Track 7 upgrade, which allows riding all trains (but not trams/buses!) after 7pm for free. Depending on how you plan your trips, this may or may not pay for itself.
2.b) Local transport: For getting around the Zurich/Wintherthur region, you'll probably need a ZVV monthly travelcard for unlimited regional travel. The price for the NetworkPass depends on the number of zones you need (zone 110 and zone 120 count twice). However a pass for both Wintherthur+Zurich (6 zones) gets expensive quickly even with the under 25 discount, so you might want to see if buying day passes (valid for 24h each, the website has a typo there) is the more prudent option. Buying 6 day passes gets you a 10% discount. Day passes are cheaper with the aforementioned half-price card, but the NetworkPass is not (all monthly/yearly passes are exempt from being used with the half-price card).
If you live near ZHAW it may also be possible to buy a used bike (~200.-) to get around Winterthur. This is a popular option here for some.
2.c) Planning: Use the SBB online timetable. It works flawlessly for all national and local public transport, and departure/arrival/transfer times are accurate to the minute. You can expect the timetable to be accurate to within 1 minute. For each route, you can also check to see how expensive tickets are. If you book early (a few days in advance), you can get supersaver tickets for almost another 50% off. However, with those tickets you have to take the actual exact train you booked the ticket for, they are not valid for a later/earlier train. ZVV also has a online timetable, but the data source/search engine is exactly the same. Google Maps works, but is not as reliable as the SBB/ZV timetables:the transfer times/routes are sometimes way off.
2.d) Taxis: Never take a taxi, you cannot afford it here. On the weekends public transport operates at night, so you just need to get a night supplement ticket for 5.- in addition to your regular ticket. During the week, students usually just wait until the first train/tram at 5am, walk home, or crash on a couch at a friends place. If you ever need to take a taxi, make sure to share it with 3 other people. Taxis are metered and drivers are usually honest, but you won't really know how much a ride will cost (there is no Swiss equivalent to gothere.sg).
3) Mobile telephony is not a problem. Get a prepaid SIM card with no monthly costs (M-Budget, Orange, Sunrise), some of these allow you to get Internet for a fixed price. I'd recommend getting some sort of Internet access, as everyone uses Facebook/Whatsapp rather than texts. Use the comparison site dschungelkompass.ch "Jungle Compass" to get an overview of available tariffs. If you want to call to Singapore, it's probably cheapest to get Skype credits and call over Skype (you can call Singapore phone numbers from Skype for a few cents.
4) Me neither. I'd check if you actually need a local bank account here, or if you can use your Singapore account. If you do decide to open an account here, mention that you are a student. Student accounts usually don't incur any fees or the like, things like ATMs etc. are all free of fees for students.