Learn Hardcore Chinese: shàngwán kè yǐhòu, wǒmen qù gōngyuán sànbù. - After we finish class, we’ll go for a walk in the park.

上完课以后
The complement 完 already shows completion, so 了 is not required.
上完了课以后
Also grammatical, but sounds a bit heavier or more emphatic, often used in speech when you’re stressing that something is indeed finished.

In many Verb + 完 + Object structures, adding 了 is optional and depends on style and emphasis:

看完电影(了)以后，我们去吃饭。

What’s the difference between 上完课以后 and 下课以后? Do they mean the same thing?

They are close, but not identical.

上完课以后
Focuses on you finishing the action of attending the class.
下课以后
Literally “after class is dismissed / class ends.” Focuses more on the time when the class session ends, from the schedule’s perspective.

In everyday speech, both are often interchangeable:

上完课以后，我们去公园散步。
下课以后，我们去公园散步。

Both can mean “After class, we go to the park for a walk.”

Could I move 以后 and say 我们上完课以后去公园散步? Is that still correct?

Yes, it’s correct, and very natural:

上完课以后，我们去公园散步。
我们上完课以后去公园散步。

Both mean the same thing. The difference is only which part you foreground:

Starting with 上完课以后 emphasizes time: “After class, we…”
Starting with 我们 is more neutral: “We, after class, go to the park for a walk.”

Both word orders are standard.

Does 去公园散步 mean “walk to the park” or “take a walk in the park”?

In this sentence, 去公园散步 is understood as:

“go to the park to take a walk” → “take a walk in the park.”

Structure:

去 + place + Verb = go to [place] in order to [do something]

So:

去公园散步 = go to the park to take a walk (so the walk happens there).

If you wanted to say “walk to the park” (the walking is the way of getting there), you would more likely say:

走路去公园 = go to the park on foot / walk to the park

So:

去公园散步 → walk in the park
走路去公园 → walk to the park

Why is there no 在 before 公园? Could I say 在公园散步 instead of 去公园散步?

Both are possible, but they mean slightly different things.

在公园散步 = take a walk in the park (describes where the action happens)
去公园散步 = go to the park to take a walk (includes the idea of going there)

So:

上完课以后，我们在公园散步。
After class, we (are) in the park walking.
上完课以后，我们去公园散步。
After class, we go to the park to walk.

Your original sentence highlights the movement (go to the park) plus the activity (take a walk).

Is 散步 a verb or a noun here? Why doesn’t it need an object or a measure word?

散步 (sànbù) is a verb-object compound that behaves like a single verb meaning “to take a walk / to stroll.”

Literally: 散 (to scatter, to loosen) + 步 (step)
Functionally: “to walk around / to stroll / to take a walk”

In normal usage:

You just use 散步 as a verb:
我每天晚上散步。 = I take a walk every evening.
It doesn’t need an object or measure word in basic sentences.

You can add adverbs or complements:

散一会儿步 = take a walk for a while
到河边散步 = take a walk by the river

But in 去公园散步, it is simply the action “take a walk” done at/after going to the park.

Can I say 走路 instead of 散步? What’s the difference?

You can say it, but the nuance is different.

散步 (sànbù): “to take a walk / to stroll,” often for relaxation, leisure, or exercise.
走路 (zǒulù): literally “to walk (on foot),” more about the way you move, not necessarily for leisure.

So:

去公园散步 = go to the park for a relaxing walk.
走路去公园 = go to the park on foot (you may or may not be strolling for fun).

去公园走路 is understandable, but sounds less idiomatic and less “leisure-oriented” than 去公园散步.

Why is there no future word like 会 or 要? How do we know this is about the future?

Chinese usually relies on context and time expressions instead of changing the verb form.

以后 (yǐhòu) = after(wards), later → clearly future relative to the class.

So 上完课以后，我们去公园散步。 is naturally understood as: > After (we) finish class, we will go to the park for a walk.

You can add 会 or 要 for extra emphasis or clarity:

上完课以后，我们会去公园散步。
上完课以后，我们要去公园散步。

These sound a bit more like plans/intention, but the original is already clearly future because of 以后.

Is 以后 necessary? Could I just say 上完课，我们去公园散步?

You can drop 以后 and say:

上完课，我们去公园散步。

This is also natural. In speech, people often omit 以后 when the ordering is obvious.

Difference:

上完课以后，我们去公园散步。
Slightly more explicit/formal: “After finishing class, we go…”
上完课，我们去公园散步。
More concise/colloquial: “(Once we) finish class, we go…”

Both describe the same sequence of events.

Could we omit 去 and say 上完课以后，我们公园散步?

No, 我们公园散步 is not natural.

You need either:

A location marker:
我们在公园散步。 = We take a walk in the park.
Or a motion verb like 去:
我们去公园散步。 = We go to the park to take a walk.

So correct options:

上完课以后，我们在公园散步。
上完课以后，我们去公园散步。

But not 我们公园散步 by itself.

Can the subject 我们 be omitted? Would 上完课以后，去公园散步 be okay?

Yes, in the right context you can omit 我们.

上完课以后，去公园散步。

This would usually be understood as a suggestion or instruction:

“After class, (let’s) go to the park for a walk.”
Or on a schedule: “After class: go to the park for a walk.”

Chinese often drops the subject when it’s obvious from context (who is “we,” who is “you,” etc.). In isolation, though, including 我们 makes the sentence clearer:

上完课以后，我们去公园散步。