There are adapter kits that turn one of your car’s fuses into two fuse sockets; you pick an appropriate circuit (not overloaded already; does/does not turn off when the key is removed, etc.) and simply add the dash cam to that circuit. No cutting or splicing required - though when I installed mine I found that the cover of the fuse box no longer fits snug; it popped open a couple of times at first until I figured out how to rearrange things to fit better.
As for running the wires - I poked mine into the crease between the windshield and the seam of the headliner, and then into the seam around the door. It’s nearly invisible.
Edited to add: the adapter kit I linked to is the one I bought two years ago; it’s worked just fine for me, but better options may have come on the market since. To be honest, I bought it 'cause it was twelve bucks instead of fifty; fortunately, it’s proved to be cheap AND cheerful.
