wǒ xūyào zhǎo wǒ de tóngshì, ránhòu yìqǐ qù chāoshì.

On its own, 找 means “to look for” or “to go see (someone),” without implying success. If you want to emphasize the result (that you find them), use 找到/找见.

• Process: 我需要找我的同事，然后一起去超市。 (I need to look for/go see my colleague…)
• Result: 我需要找到我的同事，然后我们一起去超市。
• You can also say: 等我找到我的同事，我们一起去超市。

Both are acceptable.

• 我的同事 is neutral and a bit more explicit/formal.
• 我同事 is common in speech and a bit more casual. With close relationships (e.g., family terms), 的 is often dropped. With 同事, both forms are widely used.

The subject is understood from context: it means “then we go together.” Chinese often omits the subject when it’s clear. For explicitness, you can say:

• 然后我们一起去超市。
• Or specify with the partner: 然后跟我的同事一起去超市。

一起 is an adverb and goes before the verb:

• Correct: 我们一起去超市。
• Incorrect: ✗ 我们去一起超市 or ✗ 我们去超市一起

You can make it explicit with either:

• 跟我的同事一起去超市
• 和我的同事一起去超市 Both are fine; 跟 is a bit more colloquial. Keep 一起 in there to convey “together.”

Adding 先 often sounds very natural when describing steps:

• 我需要先找我的同事，然后再一起去超市。 Your original is also fine; 然后 already implies sequence.

No. Chinese doesn’t mark future with 了. Your sentence expresses a plan/need without aspect marking. Use 了 when stating completed actions or changes:

• Completed: 我已经找到了我的同事，然后我们就一起去超市了。
• Planning/sequence (no 了): 我需要找我的同事，然后一起去超市。

Typical order: Subject + time + (modal) + place + verb (+ object).

• 我明天要在公司找我的同事，然后我们一起去超市。 If you also specify the companion:
• 我明天要在公司找我的同事，然后跟他一起去超市。

Add 一下 after the verb, or use 联系:

• 我需要找一下我的同事。
• 我需要联系一下我的同事。 This makes the request/action sound lighter.

Yes. Use 一个 to indicate “a/one (colleague)”:

• Specific: 我的同事
• Non‑specific: 一个同事
• One of my colleagues: 我的一个同事