Will things sink faster in cold or hot water?

Cold water has a higher density than that of warm water (hence it is lower than the warmer parts of water in the same container). Due to its increased density, the same sinking object will descend more slowly through its warmer comparison.

A2. The last part should read ".. than through its warmer .."

And in this type of question, you should consider viscosity as well. not much different in hot or cold water, but very different in oil or treacle with temperature change.