For 2) you might want to look into :lcd. This changes the directory of the current window (there are other commands to cd for different contexts). So what I do is ctrl-w v to split, followed by :lcd /some/path and then, in that window, I can use my fuzzy finder (or :grep).

It's still quite a few commands but the advantage is that you get a buffer where all your commands should operate on $other_repo.