Punycode isn't unicode. It maps to unicode. Thus only Punycode aware AND enabled AND non-filtering URL renderers will show emoji

I'm not sure what you're referring to with periods encapsulating the emojis.
As for the letters instead of country flags, it's because of Unicode codepoints combining, since country flag emojis are a combination of two emoji country letters, when they are written separate from each other, they show up as letters on their own. Here's a short article on that.

It also happens with some others, like skin color variants that are encoded by having a color emoji and then the standard yellow emoji (or the other way around, idk), or another that comes to mind is the heart on fire, which is heart emoji + fire emoji. These are joined with the Zero-width joiner character, you can try yourself to combine them, it's like an alchemical videogame!