I am in the process for applying to college and I need help with my major/minor...?

I am interested in going to either Harold Washington College (a community college in chicago) or University of Illinois; Urbana Champaign. I don't fully understand the major/minor degree subject and was wondering if i could recieve any help. I am interested in these programs at U of I- East Asian Languages, Graphic Design, Music-General Performance, Computer Programming, and English Language. Will I be forced to take only one of the mentioned majors? If so, will I be able to take the others as minors, or are minors specifically cles that help you in areas of study in your major. Honestly, I fell asleep in cl when this was explained, and I cannot find a clear answer anywhere. I would really like to take all of these cles if possible, and split them between the days. Also, I hear that there are general math, science, etc. cles all freshman must take. If this is true, I wanted to take them at Harold Washington where it would be cheaper. Could anyone fill me in on his please?