In all your dealings in every aspect of life in Paraguay, including the banks, you should assume that the person you will speak to will only speak Spanish. You may be pleasantly suprised sometimes, and the number of people learning English is increasing, but to rely on dealing with an fluent English speaker would be foolish.
My best device is to at least obtain levels 1 and 2 of the Pimsleur series of language CDs(English to Spanish) and spend a year becoming proficient to just that standard. I did, and when I enrolled at the Idipar Language School in Asuncion I was judged to have an intermediate level of Spanish. Not enough to really do much, but sufficient to get around and interact.
For years I have stayed at the Palmas del Sol hotel, and every year I hear the horror stories of non-spanish speakers at the hotel who have spent their entire holiday in a 2km radius of the hotel because they cannot catch the buses or make themselves understood in a taxi. They can normally be found in the gardens drinking beer that they purchased in the corner shop over the road, or in the hotel restaurant every night because they can't read a menu in an outside restaurant.
Paraguay is a beautiful country, well worth getting to know, but you really need to do some preparation by learning a bit of Spanish.
Also, the simple answer to your original question is you can't open a normal banking account without residency and a Cedula. You can make a one time deposit of $5000 into a special account at one bank (that I know of) in order to obtain residency, but that's it. You can then withdraw the money after residency is obtained.
So, all boiled down
1. Learn some Spanish
2. Obtain residency and cedula
3. Open bank account
Simple
Buying land in Paraguay
