Usually, I would order a takeout, and because of that, the ice-cream is always in a half-melted state.

Well not that melted but it is starting to melt.

Like, I heard the hot air would go up, so shouldn't the ice-cream melts from where the hot air goes?

Lately, I am verreally obsessed with a kind of Matcha ice-cream sold by a milk tea shop nearby home.

"really" is better here than "very".

it has a Matcha ice-cream layer on the top and a milk one at the bottom.

Can't really explain the grammar behind it, but the "a" belongs there.

Usually, I would order a takeout, and, because of that, the ice-cream is always in a half-melt state.

You need to isolate the "because of that" with commas. I loved this sentence. "Half-melt state" describes who I am.

Well, not that melted, but it is starting to melt.

something is melted, something melts. The adjective is "melted". "Well" is an interjection, it needs to be isolated from the rest of the phrase.
The "it is" is implicit here: "Well, it is not that melted, but starting to melt" - no need to repeat it.

Then, I noticed a bizarre thing.

"something bizarre" is an alternative.

The ice-cream always melts from the bottom up, whichen I thought it should start fromat the top.

An action happens from somewhere to somewhere, hence the "from the bottom up" and things start at a certain point. The "when" feels better than the "while".

Like, I heard the hot air would goes up, so shouldn't the ice-cream melts from where the hot air goes?

Fact, like science - present tense
should + verb :remember that the "s" is because of "does - there's no "does" in this structure.
Isn't the milk layer already liquid? How could it melt? Unless it were ice cream too. Also, I think there's no air inside the ice cream and, if so, it's limited and it doesn't affect it this way. Anyways, just a thought.

{Lately I have been | These days I am} very obsessed with a kind of Mmatcha ice-cream sold by a milk tea shop nearby home.

iIt has a Mmatcha ice-cream layer on the top and milk one aton the bottom.

Is the milk layer frozen or liquid? If it’s liquid, then we would call this dessert an ice cream “float.”

Usually, I would order it {as a takeout | to go}, and because of that, the ice-cream is always in a half-melted state.

Well not that melted but it is starting to melt.

Then II’ve noticed a bizarre thing.

“Then I noticed” doesn’t make sense because, up to this point, you’ve been describing something you do frequently, not a specific occurrence.

The ice-cream always melts from the bottom, whichbut I thought the melting should start from the top.

Like, I heard theat hot air would go up, so shouldn't the ice-cream melts from where the hot air goes?

Lately I amhave become very obsessed with a kind of Mmatcha ice-cream sold by a milk tea shop nearb my home.

It is a double-layered kind.,

wit hash a Mmatcha ice-cream layer on the top and a milk one at the bottom.

I joined these 2 sentences together to improve the flow of the paragraph.

Usually, I would order a takeout, and because of that, the ice-cream is always in a half-melted state.

Well not that has melted, but it ihas startinged to melt.