Does a mixture of gases contain equal volume to that of the container they're in? Why?
Well, the word "container" means a fixed volume. Let's look at your room for example (don't take into account any openings, like doors or windows, just the walls). It has some amount of gas in it at this moment. Now, if someone decided to "push in" let's say 100 extra moles of O2 gas, then that would not change the volume of your room. The volume of the containter remains constant, no matter how much gas we put into in. 

This is also true for each component of the mixture. The oxygen in the original air of your room had the volume of your whole room, and even when we "push in" that 100 extra moles, it still has the same volume - because your room did not change. What can change then? Obviously, the pressure or the temperature can change.