I woke up about 5 minutes ago, so forgive me if I make some stupid mistakes.

1. Not sure you need calculus for this one. By "the area of the space" I'm assuming you mean volume? And I'm assuming the canister is cylindrical. 
Volume of cylinder: pir^2h, where h is the height of the cylinder.
Volume of tennis ball: Spherical, so it's 4/3pir^3. => Volume of 3 tennis balls: 4pir^3
Height of cylinder, assuming the ends of the canister are tangents to the curves of the outermost tennis balls: 3D, or 6r. Volume of cylinder is therefore: 6pir^3.
Volume of space unoccupied by balls: 6pir^3 - 4pir^3 = 2pir^3.
2pir^3 = 2pirr^2 = piDr^2 = Cr^2 (where C and D are circumference and diameter.)

2. A few questions before I start this one: firstly, by "a quarter" of the way up, do you mean in terms of displacement or distance, or in some other way? And are we considering gravitational or frictional forces, or treating this as a non-physical scenario where the example of the cyclist and the hill is for convenience's sake?

3. So, we know they won 21 games and lost 61. Other than that - and this is probably just another example of me being incredibly stupid this soon after waking up - I think we need more information. Maybe it'd be possible to set up a general equation if I thought about it, but deciphering the specifics would be a case of trial and error, I think. Please, someone correct me if I'm wrong and I'll have a proper crack at it.

4. I agree with MDK. For some people, it's a life-changing experience that does them an enormous amount of good. For others, it's the most miserable and damning experience they'll ever have. It only suits certain personality types, and you have to really be aware of what you'll sacrifice to do it. If you feel it's for you, go for it - but put some very long, hard, careful thought into it before committing.