solution is evaporating quite quickly
 

Now that it is getting warmer, I notice that my nutrient solution is evaporating quite quickly. My question is when I am replacing the water, should I put pure water in, or water plus nutrients? It seems like the nutrients would still be in the tank since they won't evaporate, so I don't want to burn the plants with too much juice.

No you always add solution when you add water to keep the same strength. Just don't add as much.