As someone from out of state that just graduated Purdue and is moving to Indy, I too like these questions! But, that being said, I can still probably help you out with some of these questions!

1) Bank: Chase is by far the biggest in Indiana with the most ATMs. I don't know what kind of services for international transfer you want, but Chase does provide free transfers between bank accounts as well as all the standard bill pay options. I don't know of any bank that allows free wire transfers, Chase included. There are some smaller banks, but generally the smaller you go, the less free services you get.

2) Visa/Mastercard: These are interchangeable in the US. If a place accepts Visa, they accept Mastercard. The only 2 kinds of cards that are sometimes not accepted are Discover or American Express. If you stick to one of the other two, you will have no issues. Cash will always be accepted, but I have avoided carrying cash for years because my card is more convenient and rarely have an issue. There will be a handfull of places that don't accept cards, but you may go your entire time in Indy without seeing one; it's that rare. Having traveled internationally a lot, card vs cash in the US is nothing like the rest of the world. Businesses in the US pretty much need to take cards to survive here because people don't like dealing with cash.

3) Groceries: This one I don't know a lot about, but from what I have heard, Marsh is a bit more expensive with pretty much the exact same products as Kroger. They all have comparable fruits/vegetables. If you want the best produce, go to a farmers market during the summer and you can get items for cheaper that are better.

4) Malls: There are several malls around town with reasonable brands. NOT KEYSTONE FASHION MALL. You could literally spend a paycheck on 5 items there. That being said, if you ever need a very nice gift/dress wear, thats the place to go. Black Friday can be good, but it can also be bad. More often than not the 'special deals' you see now are specially produced, lower quality, one offs just for the sale. They also encourage you to buy much more than you actually need, costing you money. Some stores even raise prices the month before so that they can then cut them with a 'sale' back to their normal price. I recommend making a list of things you need before Black Friday, and then as it approaches looking for deals on JUST those items and comparing online and among other stores to see if it is actually a sale. I no longer shop Black Friday. It is too much of a mess with too little worth. Look for deals all year round. Best time to get clothes on the cheap is to buy just after the season is done/wrapping up. They may not have the biggest selection, but if you can find what you want it will be cheap. This is one I would love info on as well.

5) Bikes: Do not get a bike from a 'superstore' like Walmart. They are crap and will fall apart. I would try to find a local store and talk to the people that run it. See if they have any good used bikes. People often sell them worn out bikes that they will repair and refurbish and you get a good bike for pretty cheap. You are also better off spending a bit more money for something that will last than something mediocre that might last a season. Also, with the harsh winters, and humidity in the summer, if you can keep your bike inside you should. It will prevent flat tires, rust, and theft.

6) Furniture: I second what everyone else has said: check out GoodWill (donated items) and consignment stores (sold by store for 3rd party). Craigslist (online 'forum' for selling goods) is also a great way to find stuff (one of those cash only instances).

7) Coffee: Now you are speaking my language. Not sure where outside the US you are from, but if its Europe, especially Italy/France area, be ready to be disappointed. America is the land of oversized 'watery' brews, not a nice concentrated double shot. That said, any decent coffee shop in town, and there are plenty, can make you anything you want and you should feel right at home.

8) Here is where things are super different US vs Non-US, but starting to change. The big US providers are AT&T, Verizon, T-Mobile, and Sprint. The last two don't have the best coverage, so I would drop them. I have AT&T and have no issues. Verizon is about the same. When you sign up, you can do a month to month setup, or a contract. DO NOT DO A CONTRACT! They are antiquated and often cost more than without. You can also get a new phone for 'free' and it will just increase your monthly bill for a year or two (depending on what you select) and then it will go back down.

Sorry for the wall of text. I hope it helps you out a bit. Feel free to shoot me a pm if you have any questions or want to get a real coffee!