Why is VLC verified every time I open a file that is supposed to open with it

The hard-drive looking thing on the desktop is a mounted disk image; the .dmg file is the file where the data for the image is.

To get rid of the image, unmount it. There are three four five good ways to do it:

1. Drag the disk to the trash. The trash will turn into an eject icon while dragging.
2. Highlight the disk on the desktop and select File > Eject in the Finder menu bar.
3. Highlight the disk on the desktop and press Command-E.
4. In any Finder window, press the Eject button next to the disk in the sidebar.
5. Right-click (or control-click or two-finger-click) on the icon and select Eject. (from JoshHibschman in the comments below)
6. You can also eject from the commandline using diskutil if you really want.

After you eject the disk

Insofar as the application "file" is concerned, there is only one copy of the application: the one in the /Applications folder. The icon in the dock is only a link (not really a shortcut, as there's no file like a shortcut in the Start menu or the Quick Launch bar, but it's not bad to think of the Dock icon as a "shortcut".)

And to answer your first question, this is a great place to come with questions. Hope you have a good time on the Mac!

This is the downloaded disk image. Many applications downloaded from the internet will come as an internet ready disk image, which means that it mounts and opens when the downloaded file is opened.

A disk image is a mountable image of any volume. Disk images can be images of physical volumes or virtual disks. Like a zip, dmg disk images can be compressed (and usuall are, especially internet ready disk images such as the disk images used to install software from the internet) or can be read/write like an actual disk. They are mounted in the same mount point as physical disks, but are virtual. When unmounting, the disk is ejected and the mount point deleted like a physical disk. As the disk image is a disk, it will be shown on the desktop if you have the relevant option selected in Finder preferences:

Copy the app to your /Applications folder (or wherever else you desire) then eject the disk image by right-clicking and selecting Eject (or through Finder). The mounted disk image is the .dmg that you downloaded, therefore can be deleted by deleting this disk image after unmounting.