1-3. It's true, science can't deal with subjective stuff. It's simply not designed to do that.
4. I generally take the stance that if you can't observe a force/object/entity or its effects, it doesn't exist in any meaningful sense. Obviously, some people disagree, but I guess that's one of those subjective things. You can't really prove the value of objectivity or logic or anything like that without taking it as an assumption that such things are how to judge things.