Learn Hardcore Chinese: Wǒmen yì chīwán wǎnfàn jiù qù gōngyuán zǒu yíxià. - As soon as we finish dinner, we go for a walk in the park.

So 我们一吃完晚饭就… literally means “As soon as we finish dinner, we (then) …”.
Compared with an English “after”, 一…就… emphasizes immediacy: one thing follows directly after the other, with little delay.

Why is there a 一 after 我们? Can I leave it out?

Here 一 is not the number “one” in meaning; it’s part of the grammar pattern 一…就….

With it: 我们一吃完晚饭就去公园走一下。
→ “As soon as we finish dinner, we go to the park for a walk.”
Without it: 我们吃完晚饭就去公园走一下。
→ “After we finish dinner, we (then) go to the park for a walk.”

Both are grammatical.
The version with 一 (一…就…) makes the action sound a bit more immediate / tightly linked.
The version without 一 is slightly more neutral: “once we’re done / after we finish”.

What exactly does 吃完 mean, and how is it different from just 吃 or 吃了?

吃 = to eat (no information about completion)
吃了 = ate / have eaten (completed in time, but not necessarily “finished all of it”)
吃完 = to finish eating, to eat until it’s all gone / done

完 is a result complement meaning “finished, completed”.
Putting it after a verb means the action reaches a finished result:

看完 = finish reading / watching
写完 = finish writing
吃完 = finish eating

So 吃完晚饭 focuses on “the dinner is completely finished.”

Why is 完 placed after 吃 and not before it?

Result complements like 完 always come after the main verb:

吃完 (finish eating)
写完 (finish writing)
看完 (finish watching/reading)

You can’t say 完吃晚饭 in normal Mandarin; that would be ungrammatical.
The basic structure is:

Verb + Result complement (+ Object)
吃完晚饭
eat finish dinner

Why is it 吃完晚饭, not 晚饭吃完 here? Is 晚饭吃完 wrong?

Both can be used, but the focus and the typical patterns are different.

吃完晚饭 = “finish eating dinner” (normal neutral wording)
晚饭吃完(了) = literally “the dinner is eaten-finished”, which can sound like:
- emphasizing 晚饭 as the thing that is now finished
- often appears in slightly different structures, e.g.
  晚饭吃完了，我们就去公园。
  “Once dinner is finished, we go to the park.”

In your sentence, 一吃完晚饭就… is the most natural way to form the 一…就… pattern.
You could say 我们晚饭一吃完，就去公园…, but that’s less common and changes rhythm/emphasis.

What does 就 do here? Could we remove it?

就 often marks:

a quick or direct consequence
a natural next step
sometimes a sense of “then / right away / so / exactly”

In 一吃完晚饭就去公园走一下, 就 links the first action to the second:

As soon as we finish dinner, we then go to the park…

If you drop 就:

我们一吃完晚饭去公园走一下。

This is not standard; with 一…就…, 就 is normally required.
Without 一, you can still keep 就:

我们吃完晚饭就去公园走一下。 (correct)

So with 一…就…, the 就 is a key part of the pattern.

How do we know whether this sentence is talking about the past or the future?

Mandarin doesn’t mark tense the way English does.
This sentence by itself could mean:

“As soon as we finish dinner, we go to the park for a walk.” (habit / plan / rule)
“As soon as we finished dinner, we went to the park for a walk.” (past event)

Which one it is depends on context (time words, what was said before, etc.). You can add markers if needed:

昨天我们一吃完晚饭就去公园走了一下。
Yesterday, as soon as we finished dinner, we went to the park for a walk.
今天晚上我们一吃完晚饭就去公园走一下。
Tonight, as soon as we finish dinner, we’ll go to the park for a walk.

What does 走一下 mean here? Why not just 走?

走 literally means “to walk”, but in this context 去公园走一下 means something like:

“go to the park for a (little) walk”
“go take a short stroll in the park”

一下 adds two main ideas:

The action is brief / light (“a bit”, “for a short while”).
It makes the verb sound softer and more casual; without it, 去公园走 can feel abrupt or slightly too bare in everyday speech.

So:

去公园走一下 ≈ “go walk in the park for a bit”
Just 去公园走 is understandable but less natural in this everyday tone.

What exactly is 一下 grammatically, and why is it so common after verbs?

一下 is a verb complement that often means:

“once”, “a little”, “for a short time”

It’s used after verbs to:

indicate a short, light, or tentative action:
- 想一下 = think about it a bit
- 看一下 = have a quick look
- 试一下 = try (it) a little
soften a command or request:
- 你帮我看一下。 = Could you have a quick look for me?

In 走一下, it suggests “take a short walk” and keeps the tone friendly and casual.

Could we say 走走 instead of 走一下? What’s the difference?

Yes, you can say:

我们一吃完晚饭就去公园走走。

走走 and 走一下 are very similar in this kind of sentence:

both mean “walk a bit / go for a walk / stroll around”
both sound casual and relaxed

Nuance:

走一下: slightly emphasizes “do it once / briefly”.
走走: a reduplicated verb, feels very natural and colloquial, with a sense of light, easy action (“stroll around a bit”).

In daily speech, 走走 in 去公园走走 is extremely common.

Could we use 散步 instead of 走一下? Would the meaning change?

Yes:

我们一吃完晚饭就去公园散步。

散步 literally means “to take a walk / go for a stroll” and is a fixed word for that activity.

Nuances:

走一下 / 走走: literally “walk a bit”; very colloquial; can feel a bit more casual.
散步: “take a walk” as a specific activity; slightly more standard / neutral in tone.

In this context, all of these are natural:

去公园走一下
去公园走走
去公园散步

They differ more in style than in basic meaning.

Why is 一 pronounced yì in 一吃完 but yí in 一下?

The character 一 changes tone (tone sandhi) depending on what follows.

General rule:

Before a fourth-tone syllable → yí (second tone)
- 一下 → yíxià (下 is fourth tone)
- 一顿 → yídùn
Before a first, second, or third tone syllable → yì (fourth tone)
- 一吃 → yìchī (吃 is first tone)
- 一次 → yícì? Actually 次 is fourth tone so here it’s yí cì (this follows the “before 4th tone → yí” rule)
- 一起 → yìqǐ (起 is third tone)

In your sentence:

一吃完 → yìchīwán
一下 → yíxià

So the different pronunciations come from this tone-change rule for 一.