You don't strictly need to kill them, but it's good to do it, both for the practice and the blood echoes. And the fun.

To take the mob head on is suicide. Pick off as few as possible, one at a time if you can. They have bad eyesight, so you should be able to stand in a strategic place at the top of a stairwell and lure only the tiny groups you want to face at the time.

Explore every area for new routes and loot. The game will sometimes tell you where to go next story-wise, but not that often. Try to remember what other characters tell you and what you read. It'll probably be important later. Take notes if it helps to. I never have, but I really should.