Understanding view matrix
There is no relation between direction's direction and the world axis. And that's fortunate otherwise it would mean your camera is not a free view, it's some kind of a axis bound camera, which has its usages but most likely nothing in your mind right now.

The default camera matrix is looking at +z when everything is Identity, that's most surely where you got confused. Know that this is purely a convention, but sticking to a widely adopted convention allows for easy compatibility with libraries like glm.

the direction vector goes outward, so its normalize(lookat - campos). 

The view matrix can be constructed directly with TBN vectors in rows 0 1 2 :)
(that's your RUF)

Point 2. There is no translating of the camera to the origin, that's just how you chose to view (pun) it. There is translation of world objects toward the origin. Because the rasterizer will work in device coordinates (NDC) which is not configurable, so having a roaming camera (that travels) makes it necessary to indicate its translation in world as part of the last row (row 3), and in reverse since it's not a world matrix representing the camera position, it's the matrix that will bring back points into the view space. (by the way, incidentally meaning the actual camera world matrix is the inverse of the view matrix).


oh, that was the last phrase of pt 2.