"~" is UNIX/Linux shell shorthand for "my home directory". "~/mysql-init" is the same as "$HOME/mysql-init" except the former works even if you unset the $HOME shell variable.
You need to give the full location of that init file.
"USING PASSWORD: YES" means you specified a password when trying to connect. This is done with the "-p" option to most MySQL commands.
You can use "-pxxxx" (note there must be no space in that) or "--password=xxxx", or just "-p" and then type the password when it prompts you. Then it'll change to "USING PASSWORD: YES". Of course, you only see the error if you give the _wrong_ password. :-)
If you just hit return after being prompted for a password, it still counts as "USING PASSWORD: NO".
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