Learn Hardcore Korean: hoeuiga kkeutnago naseo dongryowa iyagihaeyo. - After the meeting ends, I talk with a colleague.

회의 = “meeting”
-가 = subject marker (marks 회의 as the thing doing or undergoing the action)
끝나다 = “to end”
-고 = connective ending “and/then”
나서 = “after (doing something)”
Altogether, 회의가 끝나고 나서 literally means “after the meeting ends.” It sets up a sequence: first the meeting ends, and then something else happens.

Why use -고 나서, and how is it different from 끝난 후(에) or 끝나면?

-고 나서 emphasizes a clear sequential action: “do A, and only after that do B.”
끝난 후(에) (“after it ends”) is a noun-form phrase (후 + 에) and is more formal or written. You’d say 회의가 끝난 후에 동료와 이야기해요 with the same meaning but a slightly stiffer tone.
끝나면 (“when/if it ends”) uses the conditional/time-marker -면, implying “as soon as it ends” or “if it ends.” It’s less about strict sequence and more about timing or condition.

Why is 회의 marked with -가 instead of -은?

-가/이 mark the grammatical subject—the doer or undergoer of the verb. Here, 회의 is what’s ending, so it takes -가.
-은/는 are topic markers, highlighting contrast or what you’re talking about generally. If you said 회의는 끝나고…, you’d be shifting the focus to “as for the meeting…” or contrasting it with something else.

What does 동료와 mean, and why is it not 동료를?

와/과 = “with” (marks a companion)
-를/을 = object marker (marks a direct object)
You’re having a conversation with a colleague, not doing something to a colleague, so you use 동료와 for “with a colleague.”

Can I use 동료랑 or 동료하고 instead of 동료와, and is there any nuance?

Yes. 랑 and 하고 both colloquially mean “with” (the same function as 와/과).

동료랑 이야기해요
동료하고 이야기해요
These are more casual or spoken, whereas 동료와 is slightly more formal or written. The meaning is effectively identical.

What’s the difference between 말해요 and 이야기해요, and why is 이야기해요 used here?

말하다 = to speak or say something (often one-way: “I say X”)
이야기하다 = to converse or tell stories (two-way interaction or chat)
Since the sentence describes having a conversation with a colleague, 이야기해요 (“chat/talk”) is more natural than simply 말해요 (“say”).

How is 이야기해요 conjugated from 이야기하다 in polite style?

Base verb: 이야기하다
Drop -다, giving the stem 이야기하-
Add the polite ending -아요/어요. Because the stem ends in 하, you use -해요.
Result: 이야기해요

Why is the verb in the present tense 이야기해요, even though the meeting ends first?

In Korean, the present tense can describe:

A habitual action (“I usually talk with my colleague after meetings”)
A planned or scheduled sequence (“When the meeting ends, I will talk with my colleague”)
So 회의가 끝나고 나서 동료와 이야기해요 naturally conveys either a routine or a scheduled plan, even though the actual “talk” follows the “end” of the meeting.