Predicting colors of aqueous solutions
There is no simple way to predict beforehand as far as I know. This is a general knowledge type of chemistry question, you will have to know or memorize the colors of common anions and cations. It will be much easier, if you do so group wise and know the colors of the first row of transition element ions.

Any object which absorbs a certain portion of visible light's spectrum, will appear colored to us. For colored solutions, we will always consider absorption of light in the visible region. So if you see a green solution, it is not reflecting green light, it is absorbing a certain portion of the visible spectrum and the transmitted light [from the solution] appears green to us. Keep this concept in mind because a lot of students have this misconception.

You should know that sulfate ion is colorless but copper (II) ion is blue so most likely copper sulfate solution is blue. In part c, you should know the color of potassium ion and dichromate ion and then guess the color. Do the remaining exercise for others.

It will be very difficult to predict if both ions are colored because it is not like that we are mixing two paints, a yellow paint with blue paint will show a green color. You will have to study the absorption spectrum of that salt. The theory of color of ions and that of solids is quite complex. It was developed by physicists. You can start from crystal field theory if you wish to see how the color of transition metal ions is explained but I will not recommend that you explore it if you are in school.