Ubuntu – What does Vi stand for

It's a parameter for the Exec key in .desktop files (defined in the Desktop Entry Specification) that describes how arguments to the program (from the file manager/program launcher, e.g. multiple selected files) should be handled:

%u A single URL. Local files may either be passed as file: URLs or as file path.

%U A list of URLs. Each URL is passed as a separate argument to the executable program. Local files may either be passed as file: URLs or as file path.

So, e.g., /usr/share/applications/gedit.desktop contains:

Exec=gedit %U

which means that arguments to gedit will be treated as a list of URLs (or local files).

For a complete list of possible parameters, see The Exec key.

The ~ and $ are elements of the command line prompt. This indicates that your computer (or more exactly, I guess, the shell you are running) is waiting for user input. It is prompting you to input a command.

The $ is merely a separator or divider. It separates the command prompt from the command which follows it. When people write such things as $ sudo apt-get update (your example), they are simply telling you that the command, in this case sudo apt-get update, needs to be entered at a command prompt. Strictly speaking, perhaps, the $ is redundant in this context.

Other separators may be used in other situations. For example, # is used for a root shell.

The ~ (called 'tilde') is shorthand for your home directory. When it appears in a command prompt, e.g., user@hostame:~$, it indicates that the current working directory is your home directory. Thus if you run the list command, ls, without specifying any particular directory, it will list the contents of your home directory.

(By the way, $HOME, is not a command, as you suggest, but rather an environment variable. It determines the location of your home directory. You can see its value by running $ echo $HOME.)