Full disclaimer, a lot of what I’m about to show is inexplicable.
The mochis are supposed to be wacky, abnormal, and
irrational. There’s no clear-cut answer as to why exactly they exist in Hetalia. They’re simply a theme in the
manga that don’t have much sense to them.

On the other hand, despite how minimal it is, there are some
explanations I can offer about what the
mochis are.

What are the mochis based on?: 

The mochis are otherworldly characters.

Ex: Estonia is brought to their world in his dreams.

Of course, their physical design is literally based off
Japanese rice balls. Each mochi represents the characteristics of their respective
nation. As such, they are also able to procure flags on a whim.

On top of that, it appears that Hima’s depiction of the
mochis is a play on words for emoticons and emojis.

They’re rice balls (mochis) that have personality (emotions).

Mochi + emotions = emoji [emochi].

Ex: The mochis are described as being based off an emoticon
Hima received in an email. [x]

Ex: Hima posted Hetalia-inspired emoticons made by fans on his blog. [x] [x]

Estonia’s involvement with them: 

Estonia initially purchases the mochis off an online auctioning site. 

The reason I believe that it’s Estonia who owns them is simply
because he’s an IT nation. A large area of information technology are computers
and the internet.

Ex: Estonia has a blog, “as befitting of an IT empire.”

If the mochis are living beings meant to represent emojis,
it would make sense that Estonia, as a nation that specializes in computer technology,
would be paired with them.

Some internet-related things would include…

Ex: Mochi Spain initially appearing with a speech bubble on
the side of his head, although this later turns out to be a cookie… (?)

Ex: The fact that the mochis swear so much. Perhaps this is
supposed to represent the unfiltered profanity of the internet. They do have
their own native language, though.

Other than that, there’s not much that I personally understand
about the mochis given how bizarre they are.

Things about the mochis that we’ll probably never make sense of:

The leader of the mochis refers to Estonia as Holy Bitch.

Amerimochi thinks that a head of lettuce is his father.

The mochis can have legs and arms.

You get 500 million experience points if you defeat a
mochi.

The mochis were weird enough to scare aliens. Hima’s fully aware of what he’s doing.

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Much of the existence of the mochis, if I’m going by Hima’s trolling type of humour, is meant to be weird and inexplicable.

However, there is some logic to it and I’d be happy to explain what little there is that I understand about the mochis. All around, it’s just bizarre lol. There’s no clear-cut answer. 

Post on the mochis coming up tonight!

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Misconception: He’s
Iceland’s father.

Reality: He
raised Iceland and acts as an older brother figure/ mentor.

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Ex: He supportively
encourages Iceland to participate in their activities. In this case, they’re
designing a Nordic-inspired hotel.

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Ex: He also gave young Iceland diplomatic advice.

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Misconception: He’s a playboy that treats Norway like a
loose end

Reality: Denmark treasures Norway as his best friend. As the
leader of the Nordics, he’ll selflessly put others first before himself.

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Ex: When Denmark realizes that Norway is struggling under
his rule, he breaks down crying.

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Ex: Denmark gets distressed when he’s forcefully separated from
Norway by a British Naval Blockade. He’s more worried about Norway.

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Ex: He doesn’t want to let Norway down and look “uncool.”
Because of this, he heads into a battle with Sweden that he knows he’s going to lose.

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Notice how he still tries to set an example for Norway.

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Misconception: Norway is indifferent toward Denmark.

Reality: While Norway may enjoy teasing Denmark and often gets
irritated with him, he too reciprocates this deep-set affection. The two share
a strong bond.

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Ex: Norway’s hobby is gently poking Denmark. Denmark doesn’t
even notice Norway’s comments.

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Ex: Norway expresses concern before Denmark charges into a
doomed battle against Sweden. Denmark refers to him as a “worry wart.”

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Ex: Despite how poor he is under Denmark’s rule, Norway
recognizes that Denmark’s trying his best.

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Again, Denmark may annoy Norway, but the two care strongly
for each other.

The running gag between the two of them is Denmark being
overly affectionate and Norway’s cheeky reactions to this affection.

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Misconception: He has a hot temper.

Reality

He had a hot temper.

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Due to recent statistics, Denmark is the happiest of the Nordics – his people are rated to be among the happiest in the world. [x]

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Misconception: He and Sweden hate each other.

Reality: They hated each other. 

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Aside from friendly teasing here and there, the two get along really well.

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Or, my personal favourite: Denmark and Finland mocking
Sweden.

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Bonus facts:

He has a good relationship with Germany, mostly stemming
from their economic ties.

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He once watched Hans Christian Andersen water grass with his
own tears.

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He’s one of the few nations who can get the Netherlands to
sell him goods at a cheaper price.

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