what if I bingewatch HotD

First of all, a language usually exists on different dimensions, called variations, which basically determine how and when a language is effectively used. These dimensions can be represented on a diagram:

(may vary. Also simplified. Please don't come at me for inaccuracies)

Where the black circle represents the standard form of a language and the purple area represents where I think the universal nation language stands. What does it mean?

First of all, that said language is most likely not standardised. Languages like English, French, Spanish etc all have at least one standardised form that is considered the correct way to speak and write a language, aka the language you would use when talking to non native speakers, or at school/work. The language you use when talking to family and friends or, for example, when writing an essay is probably vastly different from that standard form. The circle would be lower to the right in the first case and higher to the left in the second case.

The universal nation language, as I see it, would most likely not have something like that, as it’s restricted to the lower right quadrant (informal, spoken, casual). This means it probably does not really have a written form either, or if it does, it’s very inconsistent, which brings me to my second point: the universal nation language is subject to a lot of regional changes. There is most likely not one language, but rather different individual languages that exist on a spectrum and share enough characteristics that make them mutually intelligible. It would be unrealistic to think that a language spoken by nation-beings all around the world would sound the same everywhere. Now unfortunately, describing these characteristics is out of my capabilities, I’ll leave that to any conlangers who’d like to delve into this mysterious language and try to bring it to life. I can, however, try to describe a few general traits I think it might have:

1. It’s used for communication among nations who speak different languages. This is an obvious one: you meet a fellow nation, but neither of you speaks the other’s language, so you resort to the one you both are sure to know. In human terms, it’s the same as people resorting to English when they don’t know each other’s language, even if English is not their native language itself.

2. It's passed down from nation to nation. Because it does not have a stable written form and is only used among nation-beings, a nation can only learn to speak the universal language if he/she grew up around at least one other nation who speaks it. This means that if a nation grew up isolated or with minimal contact with other fellows, they're probably going to struggle with this universal language.

3. It is used in discussions during meetings, although the final documents (if there's any) will be redacted in English or some other human language. Obviously, in the case of meetings where humans are also present, then a "normal" language is used.

4. Related to the former point... Nations use it when they want to avoid being eavesdropped on by humans. The universal nation language is probably extremely inaccessible to humans, which means the nations will resort to it if they want to avoid being understood by humans in some contexts, even if they share a language and could easily communicate in it.

This does not mean that nations do not bother to learn each other's languages or that they only ever speak in this universal language, it just means that they have a common language to resort to when there's no shared languages and it probably makes communication easier in situations where there's a lot of them. It's basically their lingua franca, like English for humans these days, except it does not have any official form and is only passed on orally.

As I said before, it is outside my capabilities to describe in detail how I think this language sounds, but I imagine it to be like a pidgin derived from more than a few languages, especially older ones or older varieties.

Why is that?

First of all, naturally, the first nation-beings to develop this form of communication were speakers of ancient languages. Secondly, nations have a warped sense of time— it flows much more slowly to them compared to humans, and this probably reflects in their common language. Languages evolve extremely fast, and naturally, the universal nation language spoken today is not the same that was spoken by ancient nations, but it also evolves very slowly in human terms, which would make it possible for an ancient/dead nation-being to communicate with a modern counterpart, albeit with some difficulty.

The aspect that changes the most and the fastest, just like in human language, is vocabulary. Times change, new inventions and ideas are born, and the universal nation language also naturally has to come up with new words to describe them. If a concept is unique to a certain country or culture, the word will even likely be a “loanword” from the language of said nation!

In a way, the existence of a shared universal language in the Hetalia universe is directly tied to the nature of the characters themselves: immortal beings representing nations from all over, for whom time flows differently, and who mostly grew up interacting with their own kind rather than humans. Considering the characteristics of said language, it's also interesting to consider the implications of its use (and disuse). Two nation-beings can choose to learn each other's native languages and stop using the common language as a sign of affection or closeness, or vice versa, one of them could refuse to use the common language to communicate with another nation-being in order to signal distance or refusal to communicate.