Learn Hardcore Korean: sangsado hoeuie chamseokhaeyo. - The boss also attends the meeting.

도 means “also,” “too,” or even “even.” Attached to 상사, it tells us that the boss is included in whatever group or action you’re talking about. Here it means “the boss, too, attends the meeting.”

Why isn’t there a subject marker like 이/가 after 상사? Why just 상사도?

In Korean, some particles (like 도, 만, 까지) replace the usual case markers. You never say 상사가도. Instead, you drop 이/가 and directly attach 도 to the noun.

What does the particle 에 do in 회의에?

Here 에 marks the target or location of an action. With the verb 참석하다 (“to attend”), 회의에 means “to the meeting,” i.e. the event you are attending. So 회의에 참석하다 = “attend a meeting.”

What does 참석해요 mean, and how is it different from 회의에 가요?

참석해요 is the polite present form of 참석하다 (“to attend”).
회의에 가요 just means “I go to the meeting,” while 회의에 참석해요 specifically means “I attend (and take part in) the meeting.” It’s more formal and precise.

Why is it 회의에 참석해요 instead of 회의를 참석해요?

참석하다 is intransitive and doesn’t take an object marked with 를. Instead, the thing you attend is marked with 에.

What level of politeness is used in this sentence, and how could I change it?

참석해요 is polite informal style (해요체), common in everyday speech.
To make it more formal (존댓말), use 참석합니다.
In plain style (for notes or diaries), use 참석한다.

How would the nuance change if I said 상사는 회의에 참석해요 instead of 상사도?

상사도 = “the boss, too/even.” It adds the sense of inclusion or surprise.
상사는 = “as for the boss,” simply sets 상사 as the topic without the “also” nuance. It would read more like “Speaking of the boss, he attends the meeting.”