Hi, 

q is the amount of heat, which is dependent on how much of reaction has happened. 

So, when concentrations of two reactant solutions are doubled for the same given volumes, the moles of two reactants are doubled as well. 

That means more reaction has taken place, releasing more heat. Thus, q doubles too. 

The number of moles must double when the concentrations are doubled for the given volume, since the molarity times volume will give you the moles. 

We use the same specific heat capacity for solution normally, but that's such an approximation. It will differ by the amount of solute a little. But it doesn't have such a big impact on it. Normally we use the specific heat of water for the specific heat of solution. However, if the specific heat of solution is given differently from that of water in the question, you just use the given value. 

I hope you understand fully. :) 

Thank you for saying so, Seoyun!

- Kelda