I have air cleaned my D600 sensor many times (air rocket), and wet-cleaned it only once. It worked. If it makes you feel better, remember that you are not actually touching the electronic sensor, you are touching the filter that sits in front of the sensor. Nikon says the filter is made of "silicate." (Fancy glass?) My local camera shop offers to clean sensors for free, even if you didn't buy the camera there, but I haven't tried that. (They admit they hope to sell you something while you are waiting.)
As for the white balance and Live View issues, those have not happened to me. You're shooting a test pic of something white or neutral under your lights to set the custom white balance, but the images don't look right? Have you tried shooting in RAW and adjusting the WB in a RAW editor? You shouldn't have to do that, of course, for every shot, but I can see why AUTO might not work with strobes that fire during the shot. Custom WB should work. Also, you can set the temperature exactly in the WB menus. If you're confident your lights are 5k, set it to 5k and see what happens. Or see what looks right in a RAW editor, then set the camera to that temp and see what happens.
The Live View focusing issue seems strange. I assume you are using manual focus when zoomed in on that mountain? In Live View, aren't you seeing the image exactly the same as it is hitting the sensor? In that case, the photo should be the same as what you see on the screen. In any case, even in Live View mode, the camera still drops the mirror when you take a picture so the camera can check focus, then the mirror goes back up to take the photo. If you have AF still on, the body might be changing your focus, or VR on the lens might have changed something. Or the mirror flop may have created enough vibration (if you are at a low shutter speed) to induce blur.