q/ and q: are improved versions of : and / -- when you type q: or q/ it brings up a split with your : or / history in it -- so now you can use normal vim editing commands to edit an existing command or type in a new one, and then hit return and it runs the / or : on that line.

Once you get used to using them, you will only use / or : when the search or command you want is absolutely simple and straightforward.

:normal lets you use normal commands at a command line, often used for automation or scripting stuff... so you can do :normal 5j to go down 5 lines.

C-n is just normal complete