Learn Hardcore Chinese: wǒ zhǔnbèi míngtiān zǎoshang zài qù chāoshì. - I plan to go to the supermarket again tomorrow morning.

再: again in the future, or then/after that. It looks forward. Example: 我明天早上再去超市.
又: again in the past (or in statements about what has already happened). Example: 我今天早上又去了一次超市.
还: still/yet; also “in addition” in some contexts. For plans, 还要 = still going to. Example: 我明天早上还要去超市.

Where does 再 go in the sentence?

Why is there no 了 or 过? Isn’t Chinese supposed to mark tense?

Chinese doesn’t mark tense the way English does. The time word 明天早上 already points to the future, so 了/过 aren’t needed.
了 marks completion/change: 今天早上我去了超市.
过 marks past experience: 我去过那个超市.
For future intention you can add 要/会 if you like: 我明天早上要/会再去超市.

What’s the nuance of 准备 here versus 打算, 计划, 想, 要?

准备: to prepare; to be getting ready to do something; sounds like you’re set or arranging for it. Takes a verb directly: 准备去.
打算: to plan/intend; everyday, neutral: 打算去.
计划: plan (often detailed/formal): 计划明天早上去.
想: would like to/feel like; weaker intention: 想去.
要: going to/plan to/need to; stronger or scheduled: 要去.
Avoid redundant 准备要去 in most cases; prefer 准备去 or just 要去.

Can I just say 我准备明天早上去超市 without 再?

Yes. Removing 再 removes the “again” (or “then”) meaning. With 再, you imply it’s an additional visit or a subsequent step.

What’s the difference between 早上, 上午, and 早晨? Are there shorter forms?

早上: morning in general, often earlier morning (roughly dawn to around 8–9ish), common in speech.
上午: morning before noon (roughly 9ish to 12), a bit more formal.
早晨: early morning, often literary/poetic or emphasizing dawn.
Short forms: 明天早上 → 明早 or 明儿早上 (regional/colloquial). 明天上午 is also fine depending on the time window you mean.

How is 早上 pronounced? Is 上 neutral tone?

Mainland Putonghua commonly pronounces 早上 as zǎoshang (neutral tone on “shang”).
In Taiwan Mandarin, zǎoshàng (fourth tone on “shàng”) is common. Both are widely understood.

Why is there no preposition “to” before 超市? Do I need 到 or 在?

去 already means “go (to)”, so 去超市 is “go to the supermarket.”
You can say 到超市去 (emphasizing reaching the destination), but 去超市 is simpler and very common.
在超市 means “at the supermarket” (location of an action), not movement: 我明天早上在超市买东西.
Avoid 去到超市 in formal Mandarin; it’s colloquial/regionally influenced. Prefer 去超市 or 到超市去.

Do I need a measure word with 超市?

Can the time phrase move around? Are these all okay?

Yes, all natural, with slight emphasis differences:

明天早上我准备再去超市 (fronted time; emphasizes “tomorrow morning”).
我明天早上准备再去超市 (very common flow).
我准备明天早上再去超市 (adverbial time inside the plan clause; also natural). Tip: Don’t insert 的 between 明天 and 早上 in this usage; say 明天早上, not 明天的早上 (unless modifying a following noun: 明天早上的会议).

How do I say “go one more time” explicitly?

次 (general count): 再去一次.
趟 (trips/there-and-back): 再去一趟 (very natural for errands).
回 (colloquial count of occurrences): 再去一回 (regional/colloquial). Example: 我明天早上再去一趟超市。

How do I negate this sentence properly?

Why use 去 and not 来?

去 is used when the movement is away from the speaker’s current location: 去超市.
来 is used when the movement is toward the speaker/listener’s location: 明天早上来我家 (come to my place). So unless the supermarket is the speaker’s or listener’s location, use 去.

Can 再 also mean “then/after that,” not “again”?

Yes. In sequencing, 先…，再… means “first…, then…”

先开会，再去超市. In your sentence, without an explicit 先-clause, 再 is usually read as “again” (another trip). Context decides.

Any pronunciation tips for the whole sentence (tone sandhi)?

我(3) + 准(3) → the first 3rd tone becomes a half-rising 2nd: wó zhǔn-bèi.
早(3) + 上(neutral/4th in TW): zǎo-shang/zǎo-shàng.
Full tones: 再(4) 去(4) 超(1) 市(4). A smooth reading: wó zhǔn-bèi míng-tiān zǎo-shang zài qù chāo-shì.

Do I need to state a purpose after 去, like “to buy groceries”?

Not required, but very natural if you want to be specific: