dpkg --get-selections will give a list of the currently installed packages, of course you can redirect the output to a file of your choice.
The package archive will be of little use if you have run apt-get clean or similar.
As for the vim question, I can only guess as I do not use vim (nano woohoo). I am fairly sure a standard debian installation contains the package vim-tiny. Which as the name suggests probably does not have a fully featured vim. Try and install vim or vim-full and see if that makes any difference.