Learn Hardcore Chinese: wǒ gāngcái gěi tā huí le yì fēng yóujiàn.

刚才 means “a moment ago/just now,” referring to a very recent point in the past.
Position: both 我刚才… and 刚才我… are natural. After the subject is a bit more common; putting it first makes “a moment ago” the topic.
It only refers to the past (not the future). For very similar meaning you can also say 刚 or 刚刚 (both are adverbs; 刚才 is a time word).

Why is 了 after 回, and can I move 了 to the end? Do I need 了 at all?

The 了 here is the perfective 了 (completion), placed after the verb: 回了.
Sentence-final 了 is a different 了 (change-of-state). You can have both if you’re stressing “already”: 我刚才给她回了一封邮件了 (often to correct someone or emphasize completion).
Dropping 了 after 回 usually sounds off here. 刚才 does mark past time, but 了 marks completion of this specific event. Without a number/classifier, you may hear both 我刚才给她回邮件了 (sentence-final 了) and 我刚才给她回了邮件; with 一封 it’s best to keep 回了.

What is 给 doing here?

给 (gěi) is used as a coverb/preposition meaning “to/for,” marking the recipient: 给她 = “to her.”
Pattern: Subject + 给 + recipient + verb + object. Here: 我 + 给她 + 回 + 邮件.
As a main verb, 给 means “to give,” but here it’s the preposition-like use.

Can I omit 给 and say 回她一封邮件 or 回她的邮件?

Yes. Both are natural:
- 回她一封邮件 (huí tā yì fēng yóujiàn): reply to her with one email.
- 回她的邮件 (huí tā de yóujiàn): reply to her email (explicitly to the message she sent).
With 给, you highlight the recipient; with 她的 you highlight the email as the thing being replied to.

Why use 回 and not 发 or 写? What about 回复?

回 (huí) here means “to reply (to a message).” It’s common and colloquial: 回邮件/回短信/回电话.
发 (fā) = “send”; 写 (xiě) = “write.” If you say 发邮件, you’re just sending an email (not necessarily a reply).
回复 (huífù) also means “reply,” but it’s more formal or written: 回复她的邮件 / 给她回复一封邮件.

Why is 封 the measure word for 邮件? Can I use 个 or 条?

Use 封 (fēng) for letters and emails: 一封邮件, 一封信.
个 is not used with 邮件; 条 is for short text-like messages (e.g., 一条短信/微信), not for emails.
In practice, 一封邮件 is the standard and safest choice.

Why is 一 pronounced yì here (yì fēng) and not yī or yí?

Tone sandhi for 一 (yī):
- Before a 4th-tone syllable, it becomes yí (2nd tone): 一个 (yí gè).
- Before 1st/2nd/3rd tones, it becomes yì (4th tone): 一封 (yì fēng), 一杯 (yì bēi), 一条 (yì tiáo), 一碗 (yì wǎn).
- In isolation or in ordinal forms like 第一 (dì yī), it stays yī.
封 is 1st tone, so 一 → yì.

Can I omit the number/classifier and just say 回邮件?

Yes, for the action in general: 我刚才给她回邮件了 (“I just did the act of replying by email”).
If you want to specify exactly one email, keep 一封: 回了一封邮件.
Without a number-classifier, it’s less specific (could imply the activity rather than a single counted email).

Can I say 对她 or 向她 instead of 给她?

In everyday speech with 回/回复, 给 is the most natural: 给她回邮件.
向她回复 is possible but sounds more written/formal; 对她回复 is also formal and often appears in set phrases like 对…进行回复.
For daily conversation, stick with 给.

Are there other correct word orders?

All of these are fine (with slight differences in emphasis/register):
- 刚才我给她回了一封邮件。 (topic-first)
- 我刚才回了她一封邮件。 (no 给; double-object style)
- 我刚才回了她的邮件。 (focuses on “her email”)
- 她的邮件我刚才回了。 (fronts the object for emphasis)
Avoid splitting the verb and 了 weirdly, e.g., 我给她刚才回了一封邮件 sounds unnatural.

Can I use 过 here (e.g., 我刚才给她回过一封邮件)?

No. 过 marks past experience in general (at some time before now), so it conflicts with a specific past time like 刚才.
Use either:
- Specific recent event: 我刚才给她回了一封邮件。
- Experience: 我回过她的邮件。 (no 刚才)

How do I say “I haven’t replied to her yet” or “I didn’t reply just now”?

Could I use 才 instead of 刚才 to mean “just”?

才 (cái) often means “not until/only,” implying lateness or small quantity.
我才给她回了一封邮件 tends to read as “I only (just) replied (perhaps later than expected)” or “I only replied with one email,” not the neutral “just now” meaning of 刚才.
For “just now,” prefer 刚/刚刚/刚才.

Is 邮件 here the email I sent as a reply, or the email from her that I replied to?

Can I drop the subject 我?

How is 给 pronounced here?

Standard is gěi (3rd tone). In fast speech, it may sound lighter or like a half-third tone, but the dictionary form is 3rd tone.

What’s the difference between 回邮件 and 回信?

回邮件: reply to an email.
回信: reply to a (paper) letter.
Similar structure, different mediums. You can also say 回复邮件/回复信 (more formal).