1. For the Quando or Sprint, what is a ballpark cost for a second battery?
A replacement 36v lithium battery will cost about $550 including a charger (Some vendors will sell WO the charger for about $450). The Quando lithium battery has a post/bayonet electrical connector so make sure the vendor sells with that configuration or set up the Quando with anderson connections. Alternatively, you could use a NiCAD battery and charger for about one half the cost (connector issue also).
http://ebikes.ca/store/store_ezee.php
2. If it rains, is the electric part completely shut down or does it run at some capacity?
Fortunately, the eZee controller is virtually waterproof and if you set up you wiring properly with drip loops, water should not be a problem.
Read the section named "highlights" toward the bottom of the ebikes link.
3. Is there some "drag" when just pedaling because of the electric parts?
This is a mixed bag. My Quando has only one speed and is a pig to pedal. It also is a geared motor which IMO makes it harder to pedal.
I also have an eZee kit motor on a 3 speed Breezer bike which is easier to pedal.