hoeuiga kkeutnago naseo gati keopireul masilkkayo?

Because 끝나다 means to end or to be finished, and it is an intransitive verb. That means the meeting is not a direct object being acted on; it is the thing that ends.

So:

• 회의가 끝나다 = the meeting ends / the meeting is over
• 회의를 끝내다 = to end the meeting / to finish the meeting

If you said 회의를 끝내고 나서, that would mean after ending the meeting rather than after the meeting ends.

-고 나서 means after doing or after something happens. It shows that one action happens first, and the next action happens afterward.

So:

• 끝나고 나서 = after it ends
• 회의가 끝나고 나서 = after the meeting ends

It emphasizes sequence a bit more clearly than just -고 by itself.

Yes, absolutely. That sounds natural too.

• 회의가 끝나고 같이 커피를 마실까요?
• 회의가 끝나고 나서 같이 커피를 마실까요?

Both mean roughly the same thing in everyday speech.
The version with 나서 slightly stresses after that happens or once that is done.

So -고 나서 can feel a little more explicit about the order of events, but both are common.

같이 means together.

In this sentence, it tells you that the speaker is suggesting doing the action together:

• 같이 커피를 마실까요? = Shall we drink coffee together?

It often appears before the verb phrase, like here. Very commonly:

• 같이 가요 = Let’s go together
• 같이 먹어요 = Let’s eat together

A similar word is 함께, which also means together, but 같이 is usually more common in casual everyday speech.

Here, -(으)ㄹ까요? is being used to make a suggestion: shall we ... ?

So:

• 마시다 = to drink
• 마실까요? = shall we drink?

In this sentence:

• 같이 커피를 마실까요? = Shall we drink coffee together?

This form can also sometimes mean I wonder if... depending on context, but here it is clearly the suggestion/invitation meaning.

Not exactly in the same way as English will.
The -(으)ㄹ part is related to future or non-past possibility, but -(으)ㄹ까요? is best understood here as a suggestion or proposal rather than a simple future statement.

So instead of thinking:

• We will drink coffee?

it is better to think:

• Shall we drink coffee?
• Would you like to have coffee together?

It often sounds softer and more polite than a direct statement.

Korean often leaves out subjects when they are understood from context.

In English, you usually need to say Shall we drink coffee?
In Korean, the we is already understood from 마실까요?, especially in a suggestion like this.

So even though 우리 is not present, the sentence naturally means something like:

• Shall we have coffee together after the meeting?

If you wanted, you could say 우리 같이 커피를 마실까요?, but it is often unnecessary.

를 marks the direct object of the verb.

Here:

• 커피 = coffee
• 커피를 마시다 = to drink coffee

So 를 shows that coffee is the thing being drunk.

This is very standard:

• 물을 마시다 = to drink water
• 차를 마시다 = to drink tea
• 커피를 마시다 = to drink coffee

Yes, it is polite and commonly used in everyday professional or neutral situations.

The ending -ㄹ까요? / 을까요? here is polite because it uses the -요-style level indirectly through the question form. It is appropriate for:

• coworkers
• acquaintances
• someone you are speaking politely to

It is not very stiff or highly formal.
A more casual version might be:

• 회의 끝나고 나서 같이 커피 마실까?

A more formal/businesslike version might be:

• 회의가 끝난 후에 같이 커피를 마실까요?

The base verb is 끝나다 = to end / to be finished.

The breakdown is:

• 끝나다 → verb dictionary form
• 끝나고 → ending and / after ending
• 끝나고 나서 → after ending / after it ends

So the sentence is built from the verb stem 끝나- plus the connector -고, then 나서.

Yes, it would.

• 회의가 끝나고 나서 같이 커피를 마실까요?
• 회의가 끝난 후에 같이 커피를 마실까요?

Both mean Shall we have coffee after the meeting ends?

The nuance:

• 끝나고 나서 feels very natural and conversational
• 끝난 후에 can feel a little more written, neat, or slightly formal

Both are correct and common.

Both are understandable and natural.

• 같이 커피를 마실까요?
• 커피를 같이 마실까요?

The meaning stays the same: Shall we drink coffee together?

Korean word order is more flexible than English as long as the particles and overall structure are clear.
That said, 같이 커피를 마실까요? sounds very natural as a smooth suggestion.

Yes, in natural English translation it can come across that way depending on tone and context.

Grammatically, 마실까요? is closer to:

• Shall we drink coffee?
• How about drinking coffee together?

But in real-life use, English speakers might translate the social intention as:

• Would you like to get coffee together?
• Do you want to have coffee together?

So the Korean form is a polite suggestion/invitation, not a blunt literal question about desire.

Yes. In Korean, 커피를 마시다 literally means to drink coffee, but in natural conversation it often functions like English have coffee or grab coffee.

So this sentence may imply more than just the physical act of drinking. Depending on context, it can feel like:

• Shall we have coffee together?
• Want to grab a coffee after the meeting?

That makes it a very common kind of social invitation.