1. In a normal scenario, no, it isn't. But we are talking about specifically trying to lose fat.
2. Fat is more satiating than carbs, therefore you eat less on whole. Making it easier to not eat as much. This is a matter of preference though.
3. Maybe its not absolute, but its pretty close. Its hard to burn fat reserves in the presence of insulin. See below, and the references if you don't trust wikipedia.
4. of course metabolism is relevant. its literally how many calories you burn. If you eat the same, but burn less, you will gain fat.
I do agree with you, there's more than one way to skin a cat.
Personally, I ate high carb and ran a lot for 25 years, skinny fat the whole time. In the past 5 years, its gotten worse and worse. Same diet, same exercise pattern. Overestimate how many calories you are buring while running and replenishing with too many carbs will do that. Now, I eat more fat/protein now and am more lean than I was in high school. My experience is its far easier to limit energy intake when you eat more fat and protein - you just aren't hungry. Do what works for you though, that's what's important. Just sharing my experience and limited knowledge.