No one needs to apply for the copyright for an image, you own the copyright as soon as you create it, automatically.
Just because something is available for free on the internet does not give you the right to publish it. The creator or publisher holds the rights, so you need to either (1) license it / pay for the right to use it (2) ask permission to use it for free or if you credit the creator (3) use only materials that aren't copyrighted
These laws apply to anything you publish publicly, so they don't apply to internal class assignments that are never made public. You may want to include coursework in portfolios in the future, so try not to include other people's copyrighted visuals or audio.
If you aren't allowed to publish someone else's work, then how does video game streaming work? Check out this video for an explanation:
If you are using someone else's music or audio clips you need to make sure you know what category it falls under. In the music world, paying to use someone else's work is called "licensing" or "paying royalties". You aren't paying to own it, you're paying to use it.