Learn Hardcore Vietnamese: Mặc dù đến trễ nhưng cô ấy vẫn có kế hoạch tốt cho công ty. - Although she arrived late, she still has a good plan for the company.

This is perfectly natural.
Dropping mặc dù and keeping only nhưng is not okay here; nhưng alone cannot mean “although” in this structure.

So:

mặc dù … nhưng … = very common, very natural.
mặc dù … , … (without nhưng) = also correct and common.
… nhưng … alone ≠ “although … but …”; it’s just “but …” and needs a previous sentence/clause to contrast with.

Can I move mặc dù to the middle, like: Cô ấy vẫn có kế hoạch tốt cho công ty, mặc dù đến trễ?

Yes, you can, and it’s natural:

Cô ấy vẫn có kế hoạch tốt cho công ty, mặc dù đến trễ.

This is like English “She still has a good plan for the company, although she arrived late.”

So you have several natural options:

Mặc dù đến trễ nhưng cô ấy vẫn có kế hoạch tốt cho công ty.
Mặc dù đến trễ, cô ấy vẫn có kế hoạch tốt cho công ty.
Cô ấy vẫn có kế hoạch tốt cho công ty, mặc dù đến trễ.

The difference is mostly in emphasis and style, not in grammar.
(Option 1 feels a bit more “set phrase”; option 2 is very common and slightly more compact; option 3 emphasizes the positive main clause first.)

In mặc dù đến trễ, where is the subject? Shouldn’t it be mặc dù cô ấy đến trễ?

The full, explicit form is indeed:

Mặc dù cô ấy đến trễ nhưng cô ấy vẫn có kế hoạch tốt cho công ty.

Vietnamese often drops repeated subjects when they are obvious from context. Because the main clause has cô ấy, the first cô ấy can be omitted:

Mặc dù (cô ấy) đến trễ nhưng cô ấy vẫn có kế hoạch tốt cho công ty.

This is similar to conversational English reductions like “Although (she) came late, she still had a good plan” when the subject is clear from context.

So both are grammatically correct:

Mặc dù cô ấy đến trễ nhưng cô ấy… (more explicit)
Mặc dù đến trễ nhưng cô ấy… (more natural, less repetitive)

What’s the difference between trễ and muộn?

Both trễ and muộn mean “late” and are often interchangeable.

trễ
- Very common in Southern Vietnamese.
- Neutral, everyday speech.
muộn
- More common in Northern Vietnamese and in more formal or written contexts.
- Also neutral.

In this sentence, you could say:

Mặc dù đến trễ nhưng cô ấy…
Mặc dù đến muộn nhưng cô ấy…

Both sound fine. Choice mainly depends on region and style. Southern speakers tend to say trễ more often.

Why does tốt come after kế hoạch and not before it, like in English “good plan”?

Vietnamese basic noun–adjective order is:

Noun + Adjective

So:

kế hoạch tốt = good plan
(literally “plan good”)

Other examples:

người đẹp – beautiful person
nhà lớn – big house
ý tưởng hay – good / interesting idea

You generally don’t say tốt kế hoạch in standard Vietnamese; that order is wrong for simple adjective–noun phrases.

So có kế hoạch tốt is exactly the normal pattern: verb + noun + adjective.

Why is there no một (or classifier) before kế hoạch? Should it be một kế hoạch tốt?

You can say một kế hoạch tốt, but it slightly changes the nuance.

có kế hoạch tốt
- Literally “has good plan/has good planning”.
- More general: she has good plans / is well-prepared / has good planning for the company.
- No focus on “one single plan”.
có một kế hoạch tốt
- Literally “has one good plan”.
- Puts a bit more emphasis on there being a particular plan.
- Often used when you’re talking about a specific plan or a specific number (one).

Also, Vietnamese doesn’t need an article like “a” or “the”, so many bare nouns are fine and natural without một or a classifier.

In this sentence, có kế hoạch tốt cho công ty already sounds complete and natural; adding một is possible but not necessary.

What exactly does vẫn mean here, and where can it go in the sentence?

vẫn roughly means “still / nevertheless / nonetheless”. In this sentence, it emphasizes that the positive situation continues to be true despite the negative condition (coming late).

Mặc dù đến trễ nhưng cô ấy vẫn có kế hoạch tốt cho công ty.
→ Even though she was late, she still had a good plan.

Typical placement:

Before the main verb: vẫn có, vẫn làm, vẫn đi, etc.

You can’t move vẫn freely everywhere. Some patterns:

cô ấy vẫn có kế hoạch tốt – natural.
cô ấy có vẫn kế hoạch tốt – incorrect.
vẫn cô ấy có kế hoạch tốt – sounds wrong/unnatural here.

You can omit vẫn:

Mặc dù đến trễ nhưng cô ấy có kế hoạch tốt cho công ty.

This is grammatical but weaker; vẫn makes the contrast much clearer, like English “still” or “yet”.

What does cho công ty mean here, and how is it different from của công ty or vì công ty?

cho công ty here means “for the company” in the sense of intended for the benefit/use of the company.

kế hoạch tốt cho công ty
→ a good plan for the company (benefiting the company).

Compare:

kế hoạch của công ty
- “the company’s plan” (possessive: belonging to the company).
- Focus on ownership: the plan is the company’s plan.
kế hoạch vì công ty
- “a plan for the sake of the company / because of the company”.
- Emphasizes motivation or purpose/for the sake of.
kế hoạch cho công ty
- “a plan for the company (to use / to benefit from)”.
- Very natural when you mean “a plan that will be applied to/for this company”.

In this sentence, cho công ty is the most natural to express “good plan for the company” (benefit/target).

Is cô ấy a pronoun meaning “she”, or is cô a noun like “aunt/teacher”? What’s the nuance?

In modern standard Vietnamese:

cô ấy functions as a third-person feminine pronoun = “she/her”.

Historically:

cô is a kinship/role term (paternal aunt, young adult woman, female teacher, etc.).
ấy is a demonstrative (“that”).

cô ấy originally meant something like “that young woman”, but in many contexts today it’s simply used as “she”, especially in textbooks and neutral written language.

Nuance:

cô ấy – neutral, polite, often textbook-style or written style.
cô ta – “that woman (she)” with a negative or dismissive tone.
In real conversation, people often avoid cô ấy and instead use kinship terms or names:
- chị ấy, em ấy, bà ấy, or just the person’s name (Lan, Hoa, etc.), depending on age and relationship.

In your sentence, cô ấy is a neutral, context-free way to say “she”.

Can I replace mặc dù with other words like dù, tuy, or cho dù? Are they the same?

Yes, there are several common concessive markers, with slightly different flavors but similar meaning:

mặc dù … nhưng …
- Very common, slightly “full” or neutral in tone.
dù … nhưng …
- Shorter, also common.
- Often felt a bit more colloquial/compact.
tuy … nhưng …
- Very common in both speech and writing.
- Often quite natural in everyday speech:
  - Tuy đến trễ nhưng cô ấy vẫn có kế hoạch tốt cho công ty.
cho dù … nhưng …
- Slightly more emphatic, like “even if / even though”.
- Often used for stronger or hypothetical contrasts:
  - Cho dù đến trễ, cô ấy vẫn có kế hoạch tốt cho công ty.

In your specific sentence, you can say:

Mặc dù đến trễ nhưng cô ấy vẫn có kế hoạch tốt cho công ty.
Dù đến trễ nhưng cô ấy vẫn có kế hoạch tốt cho công ty.
Tuy đến trễ nhưng cô ấy vẫn có kế hoạch tốt cho công ty.
Cho dù đến trễ, cô ấy vẫn có kế hoạch tốt cho công ty.

All are grammatical and natural; the differences are mainly style and emphasis.