Learn Hardcore Korean: sajangnimi jinjihan yaegireul hadaga nongdamdo manhi hasyeosseo. - The boss was talking seriously and then made lots of jokes.

It marks a mid-action shift: the first action was in progress and then the speaker moves to or is interrupted by the next action. So -다가 often means “was doing X, then Y happened/they switched to Y.” It’s a sequential, change-of-mode feeling rather than simple “and.”

How is -다가 different from -(으)면서?

-(으)면서 = two actions happening simultaneously (“while doing X, (also) doing Y”).
-다가 = doing X, then switching to or being interrupted by Y (sequential/change). Example:
운전하면서 음악을 들어요. (driving and listening at the same time)
운전하다가 전화를 받았어요. (I was driving, then I answered a call)

Should it be 하시다가 instead of 하다가 because we’re honoring the boss?

In careful or formal speech, yes: keep -시- in subordinate clauses too: …얘기를 하시다가 … 하셨어(요). In casual conversation, people often drop -시- in the -다가 clause, as in your sentence, and keep it in the main clause. Both are common; the fully consistent form is a bit more formal.

What’s the difference among 사장님이, 사장님께서, and 사장님은?

사장님이/가: neutral subject marker; fine in everyday speech.
사장님께서: honorific subject marker; more respectful/formal.
사장님은/는: topic/contrast marker; sets the boss as the topic or contrasts with others.

What does 도 in 농담도 add? Could it go elsewhere?

도 means “also/as well” (sometimes “even,” depending on context). Here it adds that joking happened in addition to the serious talk. You could put 도 on other elements to shift the “also”:

진지한 얘기도 하다가 농담도 많이… = he did serious talk too, and also joked a lot (listing multiple things).

Why 많이 and not 많은?

많이 is an adverb modifying the verb: 농담을 많이 하다 = “to joke a lot.”
많은 is an adjective modifying a noun: 많은 농담을 하다 = “to make many jokes.” Both are grammatical, but 농담을 많이 하다 sounds more natural.

Is 얘기 the same as 이야기?

Yes. 얘기 is the common contracted form of 이야기. Both are correct; 얘기 feels more casual/conversational. Pronounce 얘기 like “예기.”

Why 얘기를 하다 instead of just 얘기하다?

Both exist and mean the same. 얘기하다 is a single verb; 얘기를 하다 is a light-verb construction (“do talk”). In everyday speech, both are natural; the light-verb version can sound a touch more colloquial.

What level is 하셨어? How would it change in other levels?

하셨어: plain (casual) speech to the listener, but honorific to the subject (has -시-).
하셨어요: informal polite to the listener, still honorific to the subject.
하셨습니다: formal polite.
Without honorific: 했어 / 했어요 / 했습니다 (these don’t honor the subject).
Narrative/written plain: 하셨다.

Can I drop the object marker 를 after 얘기?

Yes, in casual speech object particles are often omitted: 얘기 하다가. If you use the single verb 얘기하다, you don’t use 를 anyway.

Does -다가 require the same subject in both clauses?

Yes. The subject should be the same across the -다가 clause and the following clause. Your sentence keeps the same subject (the boss), so it fits the rule.

Can I switch the order to 농담도 많이 하시다가 진지한 얘기를 하셨어? What changes?

That flips the sequence. It now suggests he was joking a lot first and then moved into serious talk. The -다가 clause marks what was happening before the switch.

Is 진지한 different from 심각한?

진지한: serious/earnest (appropriate, sincere tone).
심각한: grave/critical (often heavy, potentially worrisome). Here, 진지한 얘기 fits “serious conversation” in a neutral way; 심각한 얘기 can imply a heavier, more severe topic.

Any quick pronunciation tips for this sentence?

얘기를: sounds like “예기를.”
하셨어: from underlying 하시었어 → 하셨어; think “ha-syeo-sseo,” with a tense “ss” in -었-.
Natural phrasing groups as: 사장님이 / 진지한 얘기를 하다가 / 농담도 많이 하셨어.