Recently, I engaged in a heated argument with my husband over a minor matter.

this is perfectly acceptable, but a more common way to say it might be:

Recently, I engaged in a heated argument with my husband over something small.

I: Yes, it was in such a disarray that I was unable to even enter it.

quite acceptable again, but more natural:

Yes, it was so messy that I couldn't even enter it.

Husband: Did you discard any cardboard boxes?

more natural: "throw away" instead of "discard"

I: Yes, I disposed of two boxes.

more natural: "threw out" instead of "disposed of"

One iwas empty, while the other iwas nearly empty.

If you disposed of them, this would be understood in the past tense. Otherwise, it sounds like you only relocated/moved the boxes somewhere else.

The contents (pet bottled tea) are arranged here.

I do not know what "pet" means, but maybe it is plastic?

Husband: Where did you place the Dyson cleaner?

more natural to omit "cleaner"

It is located directly in front of you.

more natural: "right" instead of "directly"

My closet is beyond your reach.

more natural: "My closet is off limits."

Please return to the original situations.

More natural: Please put everything back.

Therefore, you lack the authority to criticize my cleaning efforts.

more natural: ...you don't have the authority...

Recently, I engaged inhad a heated argument with my husband over a minor matter.

I: Yes, it was in such a disarray that I was unable tomess that I couldn’t even enter it.

Husband: Did you discardthrow away any cardboard boxes?

I: Yes, I disposegot rid of two boxes.

One iwas empty, while the other iwas nearly empty.

The contents (pet bottled tea) are arranged here.

Husband: Where did you placeut the Dyson cleaner?

I: Where are you looking?Right there!

It is located dDirectly in front of you.

My closet is beyond your reach.off limits to you!

Please return to the original situations.Don’t touch my closet! Please put everything back the way it was!

I: (Exasperated) This flat is my property, and you have never maintained a clean closetkept your closet clean.

Therefore, you lack the authoritySo you have no right to criticize my cleaning efforts.

The following day, he carelessly crashed his car into thea pillar, making big dents oin his car’s side body.

He might havMaybe he learned that getting angry over small things can lead to a big mistake.

I: Yes, it was in such a disarray that I was unable to even enter it.

One iwas empty, while the other iwas nearly empty.

The contents (pet bottled tea) are arranged here.

In the US, we simply call it “bottled tea.” If you want to emphasize the material of the bottle, you could say “a plastic bottle of tea.” “PET” is an uncommon technical term here.

I: Where are you looking?

more natural: Open your eyes!

It is located directly in front of you.

more natural: It’s right in front of you.

My closet is beyond your reach.off-limits for you.

Please return to the original situationput everything back the way it was.

The following day, he carelessly crashed his car into thea pillar, making big dents oin his car’{the side of the car | its side body}.

Recently, I engaged in a heated argument with my husband over a minor matter.

Alternative: Recently, my husband and I had a heated argument over something trivial.

Our conversation unfolded as follows: ¶
¶
¶
Husband: Did you organize my closet?

Alternative: Husband: Did you clean out my closet?

IMe: Yes, it was in such a disarray that I was unable to even enter it.

Alternative: Me: Yes, it was so messy that I couldn't even get in there.

"Me" is typically used when referring to yourself in a dialogue.

Husband: Did you discard any cardboard boxes?

Alternative: Husband: Did you throw away any cardboard boxes?

IMe: Yes, I disposed of two boxes.

Alternative: Me: Yes, I got rid of two of them.

One iwas empty, while the other iwas nearly empty.

Alternative: One was empty and the other was almost empty.

The contents (pet bottled tea) are arranged here.

Alternative: I put the contents (bottled tea) here.

I wasn't sure what "pet bottled tea" means.

Husband: Where did you place the Dyson cleanervacuum?

Alternative 1: Husband: Where did you put the Dyson?
Alternative 2: Husband: Where did you put the vacuum?

Note: If it's understood from context that you're talking about a Dyson vacuum cleaner, you can drop "vacuum cleaner" altogether and just say "Dyson." Also, "vacuum cleaner" is commonly shortened to "vacuum."

IMe: Where are you looking?

It is located directly in front of you.

Alternative: It’s right in front of you.

My closet is beyond your reach.

Alternative 1: You're not in charge of my closet.
Alternative 2: My closet is none of your business. (Note: This very blunt and direct)

Please return to the original situationput it back the way it was.

IMe: (Exasperated) This flat is my property, and you have never maintained a clean closet.

Alternative: Me: (Irritated) This apartment is mine. You’ve never kept a clean closet, so you have no right to criticize my cleaning. (Note: combined with next)

Therefore, you lack the authority to criticize my cleaning efforts.

(see above)

He became pissed off and left the room.

Alternative: My husband became furious and stormed out of the room.

Note: Careful. "Pissed off" is actually vulgar, so it doesn't really fit with the formal style of the rest of the text.

The following day, he carelessly crashed his car into thea pillar, making a big dents on his car’sthe side bodyof it.

Alternative: The next day, he carelessly hit a pillar with his car, putting a big dent in the side of it.

He might have learned that getting angry over small things can lead to a big mistakes.

QuarrelALSO POSSIBLE: A Recent Squabble

VOCABULARY: squabble --> 喧嘩(する)
(Cf. https://context.reverso.net/translation/english-japanese/squabble )

ALSO POSSIBLE: Recently, I engaged inhad a heated argument with my husband over a minor matter.

NOTE: The original wording is also possible.

I: Yes, I disposed ofALSO POSSIBLE -- I: Yes, I threw away two boxes.

One iwas empty, while the other iwas nearly empty.

The contents (some pet -bottled tea) awere arranged there.

Please return the items to the original posituations.

IN AMERICAN ENGLISH: I: (Exasperated) This flaapartment is my property, and you have never maintained a clean closet.

NOTE: Your original is fine in *British* English.

BRITISH SPELLING: Therefore, you lack theany authority to criticise my cleaning efforts.¶
AMERICAN SPELLING: Therefore, you lack any authority to criticize my cleaning efforts.

The following day, he carelessly crashed his car into thea pillar, making big dents on his car’s side body.

He might have learned that getting angry over small things can lead to a big mistakes.