Learn Hardcore Japanese: kazokuzenin ha watasi no goukaku wo yorokobimasita. - My whole family was happy about my passing the exam.

家族全員が私の合格を喜びました。
→ Focus is more on who was happy (the whole family did), often used when contrasting with others or when identifying the subject.

Both are grammatically correct.
は = topic, background
が = subject, often carries a sense of emphasis or contrast.

What exactly does 家族全員 mean? How is it different from 家族みんな?

Both basically mean all the family members.

家族全員
- Literally all members of the family
- Slightly more formal / written-sounding
家族みんな
- Literally everyone in the family
- More casual, spoken-feeling

Example:

家族全員は私の合格を喜びました。
家族みんなが私の合格を喜んでくれました。 (very natural spoken style)

Meaning is very close; it’s mostly nuance and register (formal vs casual).

Is 家族 considered singular or plural here? Should I think my family was or my family were?

In Japanese, 家族 is not grammatically marked as singular or plural. The context and words like 全員, みんな make it clear it's talking about all family members.

English has to choose singular or plural, but Japanese doesn’t.
So you can translate naturally as:

My whole family was happy, or
All my family were happy

Both come from 家族全員 in Japanese.

What kind of word is 合格 here? Is it a verb or a noun?

In this sentence, 合格 is used as a noun meaning passing (an exam), success in an exam.

私の合格 = my passing (the exam)

There is also a verb:

合格する = to pass (an exam)

So you could also say:

私が合格して、家族全員は喜びました。
(After I passed, my whole family was happy.)

In the original, the action passing is turned into a thing (a noun) and then treated as the object of 喜びました.

Why do we use を after 合格? Shouldn’t happiness use に or something?

The verb 喜ぶ works like this:
you mark what you are happy about with を.

合格を喜ぶ = be happy about (someone’s) passing
成功を喜ぶ = be happy about (the) success
プレゼントを喜ぶ = be glad about the present / appreciate the present

So in:

私の合格を喜びました。

私の合格 is the direct object (the thing they are happy about), so it gets を.

How is 喜びました formed, and what is its dictionary form?

Dictionary form: 喜ぶ (godan verb)

Conjugation to polite past:

Dictionary form: 喜ぶ
Verb stem: 喜び
Add ます: 喜びます
Past polite: 喜びました

So 喜びました = polite past (they) were happy / rejoiced.

Casual past would be:

喜んだ

What’s the difference between 喜びました, 喜んでいます, and 喜んでいました?

All use the same base verb 喜ぶ, but the aspect is different.

喜びました
- Simple past polite
- A completed event:
  - (They) were happy / rejoiced (when they heard).
喜んでいます
- Te-form + いる in present
- Ongoing state:
  - (They) are (currently) happy.
喜んでいました
- Past of the ongoing state
- Describes how they were feeling over a period in the past:
  - (They) were (in a state of being) happy.

For a reaction to news (like hearing you passed), 喜びました is the most straightforward.

Can I change the word order, like 私の合格を家族全員は喜びました? Is that natural?

Yes, Japanese word order is flexible as long as particles are correct. These are all grammatical:

家族全員は私の合格を喜びました。 (original)
私の合格を家族全員は喜びました。

The topic 家族全員は usually feels most natural near the beginning, but moving 私の合格を in front is still okay and can slightly emphasize my passing.

However, something like:

喜びました家族全員は私の合格を。

would be strange in normal prose. Verbs usually go at the end.

Would it be wrong to say 家族全員が私の合格を喜びました instead of 家族全員は?

It’s not wrong at all; it’s perfectly grammatical.

家族全員は私の合格を喜びました。
- Sets the whole family as the topic. Neutral, explanatory.
家族全員が私の合格を喜びました。
- Emphasizes who was happy (the whole family was).
- Often used if you’re contrasting with someone who wasn’t, or if someone just asked who was happy.

So yes, you can use が; it just slightly shifts the nuance from topic to emphasized subject.

Is 私の necessary? Could you just say 合格を喜びました?

You can drop 私の if it’s obvious from context whose passing you’re talking about.

家族全員は合格を喜びました。

In a conversation where everyone knows you are the one who took the exam, this is natural.

You use 私の合格 when you want to be explicit, or when there are multiple possible people who might have passed (e.g., you and a sibling).

What’s the politeness level of 喜びました? How would I say this casually?

喜びました uses ます, so it’s polite (丁寧語), suitable for most neutral/formal conversations.

Casual forms:

家族全員は私の合格を喜んだ。
Or more spoken: 家族みんな、私が合格して喜んだ。

You’d use the original 喜びました when speaking politely to teachers, colleagues, or in writing.

How is 合格を喜ぶ different from saying 合格してうれしい?

Both express happiness about passing, but they differ slightly:

合格を喜ぶ
- Uses verb 喜ぶ
- Focus on the act of rejoicing / reacting happily to the result
- Often used about other people:
  - 家族全員は私の合格を喜びました。
合格してうれしい
- 合格して (having passed) + adjective うれしい (glad, happy)
- Focus on the emotional state of the speaker
- Very common in first-person:
  - 合格してうれしいです。 (I’m happy I passed.)

So 合格を喜ぶ describes people reacting happily to the passing;
合格してうれしい describes someone feeling glad about it, especially the person who passed.

Why is it 家族全員 and not 全家族?

In Japanese, 全 + 人 (person) is a common pattern:

全員 = all members / everyone (in a group)
家族全員 = all members of the family

全家族 is not natural. You usually put 全 before words like:

全部 (all of something)
全国 (the whole country)
全員 (all members)

For family members, the established phrase is 家族全員 or 家族のみんな, not 全家族.