I have a mouth but never speak, a belly full but never eat. Letters and packages are my daily treat, what am I?

I greet you before you speak. My tail tells truths my mouth never could. I guard your home but beg at your table. I can be fierce as a wolf or small as a shoe. What am I?

I may tame your hair With a buzz and a glide, Or outrun the storm With the wind at my side. What am I?

I strike gold in rivers without taking a step. I sweep across a scene without moving an inch. I sit on a stove, held by a handle, shaping what you make. What single word connects them? What am I?

A well-used bar, teenagers and people whose romantic partners get too close ask for this final frontier.