Spf13 is not a full Vim distribution: it's a collection of plugins and settings designed to make you feel comfortable and prevent you from actually learning to use Vim.
You must have Vim installed on your machine for spf13 to work.
I don't know and SO is not the right place for such question. Use the plugin's issue tracker.
Yes, if you decide to install spf13 you can safely remove your previous nerdtree installation.
If you are new to Vim and serious about learning it I'd suggest you to forget about spf13, nerdtree or any plugin and start from scratch instead.
If you only want an usable and powerful text editor right now, don't bother with Vim and use Sublime Text.