Coming from a functional programming background, I feel there is a profound distinction between function and method. Mainly methods have side effects, and that functions should be pure thus giving a rather nice property of referential transparency

I agree it might be nice if "function" and "method" meant what you wanted them to, but your definitions do not reflect some very common uses of those terms.

In principle, one can type these directly but you'd have to know the Unicode code points

They are a nice idea, but in practice