Learn Hardcore Chinese: nǐ gēn shéi yìqǐ qù kàn diànyǐng?

It’s a preposition meaning “with.” It introduces the companion of the action: Subject + 跟 + person + (一起) + Verb (+ Object). Example: 你跟他(一起)去看电影 — “(You) go watch a movie with him (together).”

Do I have to include 一起 (yìqǐ)? What changes if I drop it?

No, it’s optional. 一起 emphasizes doing the action “together.”

With it: 你跟谁一起去看电影？ (strong “together” feel)
Without it: 你跟谁去看电影？ (still “with whom,” just less emphasis) You cannot use 一起 alone to take an object; you need 跟/和 before the person (✗ 你谁一起去… is ungrammatical).

Why is 谁 (who) in the middle of the sentence instead of at the front?

In Mandarin, question words stay in the spot where the answer would appear (they’re “in-situ”). Here, 谁 is the object of 跟, so it comes after 跟. You can also ask: 谁跟你一起去看电影？ (Who is going with you?), which flips the perspective but keeps 谁 in the position it would occupy in the answer.

Can I use 和 (hé) instead of 跟 (gēn)?

Yes. 你和谁一起去看电影？ is natural. Nuance:

跟 is very common and feels slightly more colloquial for “with.”
和 is also common and neutral as “and/with.” Very formal alternatives: 与 (yǔ), 同 (tóng).

How do I pronounce 谁 — shéi or shuí?