Confusion on when to use mass of entire solution when performing q=mc∆T
In mcΔT, you must use the total mass of the system that is changing temperature. In this case, that is the solution. 

The same thing is occurring in the second problem. The temperature of the solution changes, and therefore the solution mass is the mass you should use.

It wouldn't make sense if the solute changes temperature but the solution it is dissolved in doesn't change temperature, does it? I find it always helps me to think about the physical process that is happening for questions like this. Always identify what your system of interest is, and the initial and final states of the system. Doing so can clear up a lot of these problems, and will also help you get through more difficult problems if you ever take a thermodynamics course.