For (2), I have the following in my .vimrc and it does close to what you've described:

  nnoremap <C-p> :FZF ~/src<CR>

I feel like there you could make it open the result in a split either by modifying this mapping command, or by hitting something other than enter once you have your target selected in the fzf window.

I just open the split first, then C-p in the split.