Learn Hardcore Chinese: wǒ zǒu dào gōngyuán ménkǒu děng nǐ. - I walk to the park entrance to wait for you.

走到 + 地方 means walk until you reach that place.
Without 到, 我走公园门口 is not grammatical; 走 by itself does not normally take a place directly as its object.
Other verbs use 到 this way too: 开到公司 (drive until you reach the company), 飞到北京 (fly to Beijing).

Could I say 我去公园门口等你 instead of 我走到公园门口等你? What is the difference between 走, 到, and 去 here?

Yes, you can say 我去公园门口等你; it is natural. The nuances:

走到公园门口等你: emphasizes the manner walking, and the fact of arriving there.
去公园门口等你: just go to the park entrance to wait, no focus on walking vs other transport.
到公园门口等你 (without 走/去) is also possible in context; it focuses on the arrival more than on the journey or method.

So the original sentence suggests you are going on foot.

Does 走 here always mean walk on foot, or can it just mean go?

In many contexts 走 means to walk (on foot), and here that is the most natural reading.

In casual speech, 走 can sometimes mean leave or go away, as in 我先走了 (I will leave now).
But when it is followed by 到 + place, like 走到公园门口, it usually means walk (to) rather than just go (by any means).
If you want to be neutral about transport, 去公园门口 is safer.

Why is the present form 我走到公园门口等你 used for a future plan? Should there be a word like 会 or 要?

Chinese verbs do not change form for tense, so 走 and 等 themselves do not show past, present, or future.

Future meaning usually comes from context or from time expressions:
- 明天我走到公园门口等你 (tomorrow I walk there and wait for you → I will walk there and wait for you).
You can add a modal for future plan or intention, such as:
- 我会走到公园门口等你 (I will).
- 我要走到公园门口等你 (I am going to / I intend to).
The original sentence, in the right context (for example, in a text message about later today), is naturally understood as future even without 会 or 要.

Is 走到公园门口等你 one long verb phrase? How does this serial verb structure work?

Yes, it is an example of a serial-verb construction: two actions in sequence with no conjunction.

The structure is: 我 [走到公园门口] [等你].
There is an implied 然后 (and then):
- 我走到公园门口，然后等你.
Chinese often just puts verbs one after another in the order the actions happen, without words like and or to.

Why is there no 在 before 公园门口? What is the difference between 我走到公园门口等你 and 我在公园门口等你?

在 marks a location where something happens, while 到 here marks a destination you reach.

我在公园门口等你: I am (or will be) located at the park entrance, waiting for you. It does not say how I got there.
我走到公园门口等你: I will walk to the park entrance and then wait for you there. It emphasizes the movement before waiting.
You would not say 我走到在公园门口等你; 到 and 在 are not both used like that in this pattern.

What is the difference between 公园门口 and 公园的门口? Are both correct?

Both can be correct, but 公园门口 is more natural in this case.

公园门口 is a common compound place word meaning the entrance of the park / by the park gate.
公园的门口 is also grammatical and slightly more explicit as the park’s entrance, but it sounds a bit heavier and is less common in a simple, everyday sentence like this.
For many location-type nouns, 的 is dropped in common combinations:
- 学校门口, 家门口, 公司门口.

What exactly does 门口 mean? Is it the door itself, or the area near the door?

门口 refers to the area at or around the entrance, not the physical door leaf itself.

It can mean right at the doorway or just outside the door / gate.
For a park, 公园门口 usually means the place where people enter, around the main gate or entrance, often where you might wait for someone.

Can I add 着 after 等, as in 我走到公园门口等着你? What difference does 着 make?

Yes, 我走到公园门口等着你 is grammatical and common.

等你: plain wait for you; neutral about duration.
等着你: emphasizes the ongoing, continuous state of waiting; it can feel a bit more vivid or emotional, like you will be there waiting and staying in that state.
In many everyday cases, both are possible, with only a small nuance difference.

Should there be 了 in this sentence, like 我走到公园门口了? When would 了 be used with 走到?

In the original planning/future context, 了 is not needed and would be odd.

我走到公园门口了 usually means I have walked to the park entrance (I am there now) – a completed action and current result.
If you are describing what you already did and where you ended up, you can use 了:
- 刚才我走到公园门口了，但是你不在。
For a future plan, you normally do not add 了 after 走到.

Where would time words go if I want to say this with tomorrow or at three o’clock?

Time expressions usually go before the verb phrase, often after the subject.

Natural placements:
- 明天我走到公园门口等你。
- 我明天走到公园门口等你。
- 我三点走到公园门口等你。
Putting the time at the very end, like 我走到公园门口等你明天, is not natural for this sentence.

Can I drop 我 and just say 走到公园门口等你 in conversation?

Yes, in context where it is clear you are talking about yourself, dropping 我 is possible.

Chinese often omits subjects when they are obvious from context.
For example, in a chat where you and your friend are making plans, you might simply say:
- 走到公园门口等你。
In writing or when context is not clear, you keep 我.