The Default settings on iTunes store the music inside the iTunes Library.
Check the Advanced tab of iTunes preferences. If "Copy files to iTunes Media folder" is set, then you can remove the old copies in the downloads folder.
For the second question, are you talking about "All My Files?"
If so, that is what is called a Smart Folder or Search Folder. That "folder" just displays all your files which it finds all throughout your home folder in one place. What you see are files that are stored in other places, but the OS uses Spotlight to search the hard drive for files that match its search criteria, and then display them all in that window. You can use the files in "All My Files" just as if they were the actual file. If you delete anything from All My Files, you will delete the actual file, wherever it happens to actually exist.