I hope I can help you also on this thread. I already replied for the Health care. We were in your same situation in Dec. 2009 when we moved here.
1. Bank: I opened a non resident account in Sept. 2009 while on holiday and after, when we got our NIEs, changed it to a resident one. We went with La Caixa, I am very happy with them. I don´t know if you can do it online, before coming here, but if not it takes very little to have it done in a branch.
2. I think La Caixa and Sabadell are quite good, don´t have any other experience with others.
3. NIEs. We have done them in the first days of being here. It took us 1 hour in our area, Estepona and it could not have been more simple. You fill in a form, show your passport, pay a tax, etc and done . You need an NIE if you want a contract for phones, etc. at least that was our case. Also, after that I recomend you go and register for the Padron in your local town hall.
4. Internet dongle. We had both options: contract and pay as you go. Both can be useless if your area does not get good coverage., For a pay as you go one you pay for the initial modem (from 30 euros to 80 euros) and after 3-4 euros/day of usage. The monthly payment contract can go up to 49 euros depending on the speed (Movistar for example). If you want it only for back-up I suggest the pay as you go one....avoid the monthly costs in case you don´t use it.
Hope this helped