Best choice: “Could you review this two-page draft by Thursday? If that timing is difficult, let me know what would work.” It states the task and deadline while preserving negotiability between peers.
Contrast: “Could you…?” is a conventional neutral request; its force comes from context, not literal ability. “Would you mind…?” can be slightly more deferential, but it takes a gerund (“Would you mind reviewing…?”) and yes/no responses can be pragmatically confusing. “I need you to…” foregrounds the speaker's requirement and often implies authority or low negotiability; it is risky for a peer unless a shared obligation has already been established.
Not interchangeable: “Would you mind to review” is ungrammatical in standard usage; use “reviewing.” Memory rule: peer + negotiable task → Could you + specific action + date + room to respond. Practice answer example: for an optional second opinion, choose “Could you take a look when you have time?” rather than “I need you to review this.”