About view matrix and frustum culling
It is  common that the camera is pointing towards negative Z, in order to satisfy right hand rule. So you need to know the convention.

As for theinverse matrix of the camera matrix. Sort of yes. You can do it. However the camera matrix is a homogeneous space. While generally our other matrixes are affine spaces. If you take care of the distinction and do the proper camera divide, if tge camera needs one. Then yes you could do that.