Today, I’d like to talk about infinitives and gerunds.

Now, we are at thea gate.

He(Describe the individual) said, “I forgot to lock the door!”

Who is he? When you use a pronoun for a person not yet introduced, it makes it unclear who you are referring to. Always describe the person before using a third-person pronoun. The reason why "we" is okay is because it is the first-person plural. You know who the first-person is (you), so no need to describe the other people described by "we." But since it switches to third-person (he), you need to describe that individual first.

Infinitive here is good!

Then he rushed to the entrance.

Now, "he" is okay to use here because you have described the individual in the previous sentence.

I'm not sure if this was meant to be an infinitive, but infinitive would need "to" to be before "rush."
"He then went to rush the entrance."

(He is thinkingthinks that the door ismay not be locked at this moment, right? .)

The "right" at the end makes the sentence a bit odd. It's more of a converstional thing to add a "right" at the end like this. For example: "I swear the professor said the midterm would be tomorrow, right?" But here, that wouldn't really fit the tone, so I used "may not" to show that doubt that "right" produces.

Gerunds are using "-ing" verbs as nouns. Right now, you are using "think" in the "-ing" form as the present tense and not as a gerund. I can't figure out a natural way to write this sentence using the gerund, but here's my best shot: "His thinking is that the door may not have been locked at this moment."

After a while, he came back and said,

“I forgot about locking the door.”

Gerund usage is good here!

ItThis means that the door was locked when hewent back to thed entrance.

“I forgot about locking the door.”

I’m not sure whether or not my understanding is correct or not.

Original is okay. I think this version sounds a bit more natural.

Is the gerund natural forin that sentence?

After the settlements were agreed and the paper was on the table, just have dupon, both leaders sign the document one the signature of both leaderstable.

I'm not entirely sure what you are trying to express here, so I'll just give me best conjecture.

Kingdom Baa’s leader said,

1. Omg!!

Try not to use "omg" outside of texting. It is not an abbreviation used outside of casual instances.

I forgot to stop/pause the atomic bomb button!

In this case,You mean to say it's still continuing to counting down?

I forgot stoping/pausing the atomic bomb button.

I forgot about stopping/pausing the atomic bomb.

LThe leader asked his/her subordinate to stop the bomb and the subordinate whispered, “Boss, boss, you already stopped it.”

Since there is both the leader and subordinate here, it is unclear who "he" refers to. It can be inferred that it is the subordinate, but to be clear write "the subordinate whispered."

LThe leader saidexclaimed, “oOh!

You can use "exclaimed" instead of just "said" when there is "!" at the end. It makes dialogue seem less repetitive.

Did I?” And he continued the second sentence, didn’t he?

I'm not sure what this is supposed to mean.

My understanding is that the first one is a dangerous situation.

SThe second one is lika situation where kKingdom mMoo might say's leader might exclaim, “oh, no, you scared me!!” And hahaha situation,” laughing all the while.

Or…, in the worst case iscenario, both are still dangerous as the bomb continuinges to counting down?

AThe action haven’s not finished yet at this moment.

Still continuing counting down.

2 (止めた) is past tense.

AThe action have dones already been done so no worries about a 爆弾.

Today, I’d like to talk about infinitives and gerunds.

Now, we arThe following scene involves two people at thea gate.

This is more natural in the US.

Then he rushed to the entrance.

(He is thinkings the door is not locked at thise moment, right? )

It's not necessary to include comments like this. I would just omit them.

After a while, he came back and said, “I forgot that I locked the door.”

This sentence was a fragment so I added the next line to complete the sentence.

“I forgot locking the door.”

I deleted this and appended it to previous line.

It means the door was locked when he backed entrancechecked.

SoIn other words, he forgot that he locked the door.

“I forgot that I lockinged the door.”

Infinitive and gerund.

I deleted this and added it to the next line.

Infinitives and gerunds: I’m not sure whether my understanding is correct or not.

「Infinitive」というのは、「辞書形」という意味です。「Gerund」というのは、「(動詞) + の」ということです。Infinitive は動詞で、gerund は名詞です。

Is a gerund natural for that sentence?

いいえ、自然ではありません。

Then… how about this?

_Kingdom Baa vs Kingdom Moo._

Since this seems like a title, I removed the period and underlined it.

After settlements wereeverything was agreed upon and the paperdocument was on the table, just have doneonly the signatures of both leaders were needed.

また、

After everything was agreed upon and the treaty was on the table, only the signatures of both leaders were needed.

Kingdom Baa’s leader said, "Oh, no!"

1. Omg!!

"omg" is used in texting but not really in formal writing.

1. I forgot to stop/pause the atomic bomb buttonlaunch!

In this case,s it still continuing the counting down?

また、

Is it still counting down?

2. Omgh, no!

I forgot to stoping/pausing the atomic bomb buttocountdown.

LA leader asked a subordinate to stop the bombcountdown and he whispered “Boss, bback, “Boss, you already stopped it.”

LThe leader said, “oOh!

Did I?” AndThen he continueds with the second sentence, didoesn’t he?

My understanding is that the first oncase is a dangerous situation.

SThe second one is likwhere kKingdom mMoo might say, “oOh, no, you scared me!!” Aand hahahathen laughs at the situation.

Or… the worst case is that both are still dangerous as continuingbecause it's still counting down?

It doesn't matter whether a situation is dangerous when we're using infinitives or gerunds.

1止めるis not pastpresent tense.

AThe action havesn’t finished yetbeen completed at thisat moment.

StillThe countinuingdown counting downues.

AThe action have dones already so nbeen done so there's no need to worriesy about 爆弾.

Today, I’d like to talk about the infinitive and gerund.

Now, we aWe're at the gate.

This sounds more natural.

Then He then rushed to entrance.

The other way is grammatically correct; however, this way sounds more natural to me.

(He is thinking the door is unot locked at this moment, right? )

After a while, he came back and said,

“I forgot about locking the door.”

This sentence is grammatically correct, but only if you add "about" before "locking".

ItThis means the door was locked when he backedwent back to the entrance.

“I forgot about locking the door.”

IThe infinitive and gerund.

Is gerund natural forin that sentence?

Then…If not, how about this?

Kingdom Baa vs Kingdom Moo.

This is technically correct, but you seem to refer to each later on as individuals; therefore, I would change it to "King Baa vs King Moo".

After settlements were agreed upon and the paper was on the table, just have done the signature ofhaving just been signed by both leaders.:

Kingdom Baa’s leader said,

I forgot to press the stop/pause button on the atomic bomb button!

This sentence didn't really make sense; however, I understood the general meaning.

In this case, still continuingWait, so it's still counting down?

I forgot stoping/pausingabout pressing the stop/pause button on the atomic bomb button.

LThe leader asked the subordinate to stop the bomb and he whispered, “Boss, boss, you've already stopped it.”

"You've" sounds more natural here, but the other way was correct as well.

LThe leader said, “oOh!

Did I?” And he would continued on with the second sentence, diwouldn’'t he?

My understanding is first one is a dangerous situation.

SThe second oncase is like kingdom mthe one where King Moo might say “oh,Oh no, you scared me!!” And hahahaIt would be a humorous situation.

Or… worst case is are both are still dangerous as countinuingg down is counting dowuing on?

1. 止めるis not in the past.

AThe action haven’tsn't been finished yet at this moment.

StillThe countinuingg down is still counting downuing.

2. 止めたis the past tense.

AThe action have done already so nis already done; so no need to worriesy about the 爆弾.

Today, I’d like to talk about the infinitive and the gerund.

Or, "the infinitive and gerund tenses".

Now, we are at thea gate.

It is better to use indefinite articles (a, an) the first time something is mentioned. Afterwards, you can use the definite article to refer to the thing (the, that, etc).

"We came across a gate. The gate was wide open. Later, we walked down a path. The path was narrow."

Then he rushed to the entrance.

(He is thinkings the door is not locked at this moment, right? )

After a while he came back and said,

“I forgot to locking the door.”

It means door was locked when he backedgot back from the entrance.

“I forgot about locking the door.”

Is (using the) gerund natural for that sentence?

After settlements were agreed and the paper was on the table, just have done the signature of both leadersboth leaders have just signed the treaty.

The second part of this sentence doesn't quite work. I've suggested an alternative.

Kingdom Baa’s leader said,

1. Omg!!"Oh my gosh!"

omg is very casual. It is usually only seen in text messages between friends or family.

I forgot to stop/pause the atomic bomb buttocountdown!

In this case, is it still continuing to counting down?

I forgot stoping/pausabout stopping the atomic bomb buttocountdown.

AThe action havesn’t yet finished yet at this moment.

SIt is still continuing to counting down.

Today, I’d like to talk about infinitives and gerunds.

or: …about the infinitive and the gerund

Now, we are at thea gate.

He saidys, “I forgot to lock the door!”

You need to choose either past tense or present and stick with it. I have chosen present, since it’s what you started with.

Then he rushed tos (back) to the entrance.

After a while he caomes back and saidys,

“I forgot I had locked the door.” or: “I don’t/didn’t remember locking the door.”

“Don’t remember locking” is OK, but “forgot locking” is not.

It means the door was (already) locked when he backedgot back to the entrance.

“Backed to the entrance” means “drove (a car) backwards to the entrance.”

So he forgot that he (had) locked the door.

“I forgotdon’t remember locking the door.”