There are many questions here, but the practical answer to almost all of them is "no".
To understand why, you have to understand what all these products are.
- full-fat raw milk is an emulsion of fat in water (plus other components which are not relevant here).
- full-fat milk from the store is also an emulsion of fat in water, but it has been stabilized so it doesn't break.
- low-fat and skim milk are the same as full-fat milk from the store, but with less fat in them.
- yogurt is milk, cultured with specific cultures
- buttermilk (old meaning) is the liquid left after churning butter, consisting of tiny pieces of butter floating in whey. It is not an emulsion. It can be cultured or not, depending on whether you soured your milk first.
- buttermilk (modern meaning) is a cultured product just like yogurt, but uses different cultures, so the taste and consistency are different.
What won't work
If you were to churn butter from raw full fat milk, you would end up with butter + buttermilk (old meaning). The result is not low-fat or skim milk, since it is not an emulsion. It is also not the buttermilk required by modern recipes. You could it for either antique recipes or drink it, but it isn't like milk.
If you try to churn store-bought full fat milk, nothing will happen, because the emulsion is stabilized.
If you try to churn yogurt, nothing will happen - Getting butter from yogurt.
What works in principle
If you want low-fat buttermilk (modern meaning), the only way is to start wih low-fat milk and culture it. The catch: you said you don't have low-fat milk.
Also, if you want your own low-fat milk, the way to go is to find some raw milk, pasteurize it yourself, then let it sit in the fridge for 2-3 days. Then remove the fat from the top. You cannot control the exact percentage of remaining fat that way, but is definitely lower than in raw milk. It is certanly not no-fat, probably closer to the 1.5%ish milk that is sold in many countries. The catch: depending on your location, it may be easier to buy 1.5% milk than to buy raw milk.