Learn Hardcore Vietnamese: Tôi sẽ gửi email cho bạn cuối tháng này. - I will send you an email at the end of this month.

sẽ is the future-tense marker in Vietnamese. It makes clear that the action (sending the email) will happen later. Technically, because of the time phrase cuối tháng này, you could drop sẽ and still imply future:
Tôi gửi email cho bạn cuối tháng này.
But including sẽ is more explicit and common in formal writing. In casual speech, learners often omit sẽ when the time reference is obvious.

Why is the phrase gửi email used? Is email a noun or a verb in Vietnamese? Could I use thư điện tử instead?

In gửi email, gửi is the verb “to send” and email is a borrowed English noun meaning “electronic mail.” You can certainly use the full Vietnamese equivalent thư điện tử for formality:
gửi thư điện tử
Some people informally treat email as a verb—saying email cho tôi or email tôi—but the standard and clearer structure is gửi email (or gửi thư điện tử).

Why do we need cho bạn? Can’t we say Tôi gửi bạn email?

Vietnamese uses the pattern gửi [direct object] cho [indirect object]. Here, cho bạn marks the recipient (“to you”). Omitting cho—Tôi gửi bạn email—sounds awkward or ungrammatical in most contexts. Always include cho when indicating who receives something.

Could we use đến or tới instead of cho—for example, gửi email đến bạn?

Yes. gửi email đến bạn is also correct, especially in formal or written styles. đến and tới both mean “to.” In everyday spoken Vietnamese, cho is the most common choice, but đến/tới are perfectly acceptable.

Can we move cuối tháng này to the beginning of the sentence?

Absolutely. Vietnamese allows flexible placement of time phrases. For emphasis on when, you can say:
Cuối tháng này, tôi sẽ gửi email cho bạn.

Is vào needed before cuối tháng này? When should we add it?

vào (“at”/“in”) is optional. Both are correct:
Tôi sẽ gửi email cho bạn cuối tháng này.
Tôi sẽ gửi email cho bạn vào cuối tháng này.
Adding vào is slightly more formal or explicit, but colloquial speech often omits it when the time reference is clear.

Why is there no classifier before email? Should I say một email?

Classifiers (lượng từ) are needed when specifying quantity—e.g., một email, hai email. In gửi email cho bạn, the focus is on the action of sending email in general, not on a count. If you want to emphasize exactly one, use:
Tôi sẽ gửi một email cho bạn cuối tháng này.

Can we drop Tôi and say Gửi email cho bạn cuối tháng này?

In informal speech, notes or text-message style, subjects are often omitted when context is clear:
Gửi email cho bạn cuối tháng này.
However, in standard or formal Vietnamese, it’s better to include Tôi. Starting with Gửi works in headings or casual reminders but less so in full sentences.

What does bạn mean here? Is it singular or plural?

bạn is the second-person pronoun “you,” usually singular and friendly. For multiple people, you’d say các bạn. In more formal or respectful contexts, you might use anh, chị, ông, bà, etc., instead of bạn.