Learn Hardcore Chinese: mén guān le, wǒ zài wàimiàn kànbùdào nǐ. - The door is closed; I can’t see you from outside.

It’s the verb-suffix 了 that marks a completed event that results in a new state. Here it means “the door has become closed (and is now closed).” It follows the verb 关, so it’s not the sentence-final 了.

Examples: 天黑了 “It has gotten dark.” 下雨了 “It has started raining.”
You could also have both kinds of 了 in one sentence to show two new situations: 门关上了，我在外面看不到你了。

Could I say 门关着 instead of 门关了? What’s the difference?

门关了 highlights the change into the closed state (“the door got closed / has closed”).
门关着 uses 着 to describe an ongoing state without focusing on the change (“the door is closed”). Both can fit, but 关了 is especially natural as a cause for the next clause (therefore I can’t see you). 关着 is more neutral, just stating the current state.

How is 关了 different from 关上了? And what about 把门关上了 or 门被关上了?

关了 = “closed/has closed” (simple, result is that it’s closed).
关上了 adds the resultative complement 上, emphasizing “closed shut.”
把门关上了 makes it explicitly transitive and agented: “(someone) closed the door.”
门被关上了 is a passive form: “The door was closed (by someone).” In your sentence, 门关了 is fine because we’re just reporting the door’s closed state as the reason.

Why is it 不 in 看不到 and not 没?

This is a potential complement pattern: V + 得/不 + Result. Use 不 to express (in)ability under the current conditions.

我看不到你 = “I can’t see you (it’s not possible from here/now).”
我没看到你 = “I didn’t see you (on that occasion)” — a past, factual non-occurrence, not inability.

What’s the difference between 看不到 and 看不见? What are the positive forms?

看不到 and 看不见 are near-synonyms in everyday speech.

Subtle nuance: 到 emphasizes reaching a result (“not able to achieve the result of seeing”), 见 emphasizes the act of perceiving (“not able to perceive”). In practice, either works here.
Positive counterparts: 看得到 / 看得见 (“can see”).

How do I pronounce 看不到 exactly? Does 不 change tone here?

Pronounce it as kàn bú dào because of tone sandhi: 不 (normally bù, 4th tone) changes to bú (2nd tone) before another 4th-tone syllable (到 dào).

Whole sentence with natural tones: mén guān le, wǒ zài wàimiàn kàn bú dào nǐ.
Note: sentence-particle 了 is a light, neutral tone (le).

Is 在 here the location preposition “at,” or the progressive marker “be doing”?

Here it’s the location preposition: 我在外面 = “I am outside.” The progressive marker 在 comes directly before a verb (e.g., 我在看书 “I’m reading”). In your sentence, 在 introduces the place, not the progressive aspect.

Can I drop 在 and say 我外面看不到你? What about just 外面看不到你?

With a personal subject, you normally keep 在 before a bare place word: 我在外面看不到你. Saying “我外面看不到你” sounds off.
You can drop the subject in colloquial speech: 外面看不到你 = “From outside (you) can’t be seen” / “Outside, (I) can’t see you.”
To emphasize vantage point, you can also say: 从外面看不到你 (“from outside, I can’t see you”).

Where can I put 在外面 in the sentence? Do different positions change the meaning?

我在外面看不到你 — neutral and most common: “I, being outside, can’t see you.”
在外面，我看不到你 — topicalized place; same meaning with emphasis on location.
我看不到你在外面 — tends to mean “I can’t see you when you’re outside” or “I can’t see that you’re outside” (ambiguous; usually avoid unless that’s the intended meaning).
我看不到在外面的你 — “I can’t see the you who is outside” (relative clause modifying 你); grammatical but more marked.

If I add 了 at the end (我在外面看不到你了), what changes?

Sentence-final 了 marks a new situation or change relative to before. 我在外面看不到你了 suggests “I can’t see you (anymore/now),” implying that previously I could or that circumstances have just changed. Together with 门关了, it reads as a freshly changed situation on both counts.

Could 门关了 ever be a command like “Close the door”?

No, it’s a statement. For a request/command, use:

把门关上(吧) — “Close the door (please).”
把门关了(吧) — also used colloquially to mean “Close the door,” though 关上 is a bit clearer for “close it shut.”

Do I need a measure word with 门 here?

Not in this sentence. But when counting, use 扇:

一扇门 “one door” In 把-constructions you don’t add the measure unless you’re quantifying:
把门关上了 (no measure) vs 把那一扇门关上了 (with a specific, counted door).

Are 外面, 外边, and 外头 the same?

They’re near-synonyms meaning “outside.”

外面 (wàimiàn) — very common and neutral.
外边 (wàibiān) / 外头 (wàitóu) — also common; 外头 is a bit more colloquial/regional in feel.
More formal/technical: 外部 (“the exterior” of an organization/structure). All work in everyday speech in this sentence.

Can I say 从外面 instead of 在外面? What’s the difference?

在外面 = “(while) outside” — locates the subject.
从外面 = “from outside” — emphasizes vantage/path. So 从外面看不到你 focuses on the viewing perspective; 在外面看不到你 focuses on where the speaker is situated. Both are fine here.

Is 门被关了 natural? Should it be 门被关上了?

门被关了 is grammatical but feels a bit bare; 被-sentences often sound better with a clear resultative complement.
门被关上了 is more natural: “The door was (shut) closed (by someone).” Use 被 when you want to highlight the affectedness or an external agent (often when it’s inconvenient or unexpected).

How can I say “I can’t see you clearly” or “I can barely see you” instead of a flat “can’t see”?

“I can’t see you clearly”: 我看不清(楚)你 or more commonly 我看不清(楚)你这个人/你的脸 (if you mean features).
“I can barely see you”: 我勉强看得到你 / 我几乎看不到你. These use different complements to express degree or clarity of perception.