Learn Hardcore Chinese: Jīntiān wǒ bùdàn kāihuì, érqiě yào mǎshàng gěi tā huí yóujiàn, wǒmen wǎnshang zài liáotiān. - Today I not only have a meeting, but also need to reply to her email right away; let’s chat again tonight.

不但…而且… means “not only…, but also…,” linking two parallel parts. In the sentence, the first action is 不但开会, and the second is 而且要马上给她回邮件.
You cannot replace 而且 with 但是 (“but/however”); that would flip the meaning to contrast instead of addition.
In speech, you’ll often hear 不但…还/也… (e.g., 不但开会，还/也要回邮件). That’s fine and natural. With 而且, the tone is a bit more formal/structured.

Why is 要 only in the second half? Should it be in both parts for parallelism?

Both are acceptable:

Current: 不但开会，而且要马上给她回邮件. This implies “I have a meeting, and in addition I (need to/am going to) immediately reply to her email,” slightly emphasizing the obligation/plan in the second part.
More balanced: 不但要开会，而且要马上给她回邮件. This makes both actions planned/obligatory. Choose based on the nuance you want.

What exactly is 给 doing in 给她回邮件? Is it a verb “to give,” or something else?

Here 给 functions like a preposition (often called a “coverb”) marking the recipient: “to/for.” Structure: 给 + recipient + [verb phrase]. So 给她回邮件 = “reply to her (by email).” Similar patterns:

给他打电话 (call him)
给老师发消息 (send the teacher a message)

Is 回邮件 the same as 发邮件 or 回复邮件? Which is most natural?

回邮件 = “reply to an email” (colloquial; very common).
回复邮件 = “reply to an email” (more formal/written or in work contexts).
发邮件 = “send an email” (not necessarily a reply). You can also say 回她的邮件 (colloquial; often the 的 is dropped: 回她邮件) or 回复她的邮件 (formal).

Does 会 here mean “will/can”? I’m confused by 开会.

In 开会, 会 is a noun meaning “meeting,” and 开 means “to hold.” Together 开会 = “to have/hold a meeting.” It’s not the modal 会 (“will/can”). So 我不但开会 means “I not only have a meeting…,” not “I not only will/can…”.

Why use 再 in 我们晚上再聊天? Why not 又 or 然后?

再 is used for repetition or a subsequent action in the future: “again/later/then (later).” 我们晚上再聊天 = “Let’s chat later this evening (again).”
又 usually describes repetition in the past or present (often with a sense of “happened again”).
然后 means “and then/after that,” focusing on sequence, not repetition. Here 再 is the right choice.

Is 我们晚上再聊天 a suggestion like “Let’s chat tonight”? Do I need 吧?

Yes, 我们 + verb can make a gentle suggestion (“let’s …”). Adding 吧 softens it further:

我们晚上再聊天吧。 = “Let’s chat again tonight (okay?).” Without 吧 it can still read as a plan/suggestion in context.

Where do time words like 今天, 马上, 晚上 go? Could I say 我今天… or put 马上 elsewhere?

Typical word order is: Time > Subject > (Adverbs/Modals) > Verb > Object.

今天我… and 我今天… are both fine; sentence-initial time (今天) is very common.
马上 (immediately) usually goes before the verb phrase it modifies: 马上给她回邮件.
For the evening plan, 我们晚上再聊天 places 晚上 before the verb phrase it modifies.

Do I need 了 to show future or completion here?

No. Chinese doesn’t mark tense like English. The future sense is given by 今天/晚上 and the modal 要. If you said 马上要给她回邮件了, that would mean “(I’m) about to reply to her email right away,” with 了 marking a change-of-state/imminence. It’s a different nuance.

Should 不 in 不但 be pronounced bú (tone sandhi)? The pinyin shows bùdàn.

Tone sandhi: 不 (bù) changes to bú before a fourth tone. Since 但 (dàn) is fourth tone, the natural spoken form is búdàn. Many materials write the underlying tone (bù) in isolation, but you should pronounce búdàn.

Should there be a measure word with 邮件, like 一封? When do I add it?

General activity: 回邮件 (no measure word needed).
Specifying quantity: 回她一封邮件 or 回她两封邮件.
In formal writing: 回复她的邮件 is common without counting.

What’s the difference between 要马上 and 马上要?

要马上 + V emphasizes the requirement to do it immediately: “need to immediately …”
马上要 + V emphasizes it’s about to happen very soon: “is about to … right away.” Both are grammatical; choose based on focus:
要马上给她回邮件 = obligation/plan to do it now.
马上要给她回邮件 = it’s imminent.

Can I drop 她 and just say 给回邮件?

No. 给 needs a recipient. You can:

Keep the recipient: 给她回邮件.
Or drop 给 + recipient entirely and just say: 回邮件 (“reply to the email”). But 给回邮件 (without the recipient) is ungrammatical.

Can I omit 而且 and just use 也 or 还 in the second part?

Yes, in speech you can say:

今天我不但开会，还要马上给她回邮件。
今天我不但开会，也要马上给她回邮件。 These are natural. With 而且, the structure feels a bit more formal or emphatic.

Is 晚上 pronounced wǎnshang or wǎnshàng?

Standard pronunciation is wǎnshang, with a neutral tone on the second syllable. You may see dictionaries marking wǎnshàng, but in everyday speech the second syllable is typically neutral.

Why does the subject change from 我 to 我们 before 晚上再聊天?

Because the evening plan involves both the speaker and the addressee. 我们晚上再聊天 = “Let’s/we’ll chat again tonight.” Subject switching across clauses is normal; Chinese doesn’t require repeating the earlier subject if context is clear, but here changing to 我们 clarifies who will chat.

Is 马上 the only option for “right away”? How about 立刻, 赶紧, 赶快, 立马?

马上 and 立刻 are close; 立刻 can sound slightly more formal/urgent.
赶紧/赶快 add a “hurry up” flavor (often imperative/suggestion): 赶紧给她回邮件.
立马 is very colloquial/regional (common in the north/west). All would be understood; choose based on tone and formality.