Are you talking about a color calibration profile, or setting your illuminant to daylight? The second will not fix your issue. The first very likely will.
In the current scene referred workflow, the white balance module should be set to camera reference, unless you have created a specific white balance profile with a calibrated monitor. As Aurelien has already mentioned in his videos, color calibration is meant as a corrective tool, not as a creative one. When white balancing, it should bring your picture to a neutral state (neutral whites, grays and blacks). If you make the white balance too warm, it will only further mess up your colors, and that info gets passed onto the other modules in the pipeline, like color balance rgb. If you want to make the picture “warmer” or “colder”, color balance rgb is the better place to do that.
Not necessarily. The default one seems broken for your camera, and I can’t speak for the a7m2 dcp one. For my camera, a custom color calibration profile has a significant impact.
If you shoot under those conditions a lot (indoors and with home lights), a custom profile for that light would give you the best results, although a general purpose one will likely already improve things for you.
I am not sure that I understand you correctly. The current workflow is the following: don’t touch the white balance module, just leave it on camera reference. Use color calibration to get a correct white balance. If the input profile is bad, like in your case, create a new one with a color checker as I explained above and save it as a preset. This can be automatically applied to all the images from the same camera. Once you do that, the only thing left for you to do when adding new pictures is to use the color picker in the CAT tab to select a neutral spot (white, gray) and that will remove any color casts. Once you set things up, it is as quick, or perhaps quicker than most other raw processing programs.
I would recommend that you watch those videos by Aurelien, and take some notes to fully grasp what is in there. That’s what I did.