Họ không những cho ăn mà còn kiểm tra.

It is a very common Vietnamese pattern meaning not only ... but also ....

So:

• Họ = they
• không những cho ăn = not only feed / give food
• mà còn kiểm tra = but also check / inspect

This pattern links two parallel actions, qualities, or facts.

Here, mà is part of the fixed pattern không những ... mà còn .... In this structure, it does not mean a strong contrast like English but by itself. It works more like the connector in not only ... but also ....

So you should learn không những ... mà còn ... as one set.

Yes. Cho ăn is a very common verb phrase.

Literally:

• cho = give / let
• ăn = eat

But together, cho ăn usually means to feed or to give food to someone or something.

Examples:

• cho chó ăn = feed the dog
• cho em bé ăn = feed the baby

So in this sentence, cho ăn is best understood as feed.

Vietnamese often leaves out objects when they are already understood from context.

So Họ không những cho ăn mà còn kiểm tra can mean:

• They not only fed them but also checked them
• They not only gave food but also did an inspection/check

The sentence is not ungrammatical without an object. It just relies on context.

If you wanted to make it explicit, you could say something like:

• Họ không những cho chó ăn mà còn kiểm tra nó.
• Họ không những cho bọn trẻ ăn mà còn kiểm tra sức khỏe của chúng.

Yes, depending on context, cho ăn can sometimes be understood as let someone eat or give someone food. But in many real situations, especially with animals, children, or patients, English usually translates it as feed.

So this sentence could be interpreted as:

• They not only fed them but also checked them.

That is the most natural reading unless the wider context suggests something else.

Kiểm tra usually means check, inspect, examine, or look over.

The best English choice depends on context:

• with machines: inspect/check
• with homework: check
• with people or animals: examine/check
• with documents: inspect/check

In this sentence, it probably means they did some kind of follow-up check after feeding.

Vietnamese verbs do not change form for tense the way English verbs do. So this sentence by itself does not clearly mark tense.

Họ không những cho ăn mà còn kiểm tra could mean:

• They not only feed but also check.
• They not only fed but also checked.
• They not only were feeding but also checking.

The time is usually understood from context, or from extra words such as:

• đã for past
• đang for ongoing action
• sẽ for future

For example:

• Họ đã không những cho ăn mà còn kiểm tra. = They not only fed but also checked.

Yes. Không những ... mà còn ... and không chỉ ... mà còn ... are very close in meaning.

So you can also say:

• Họ không chỉ cho ăn mà còn kiểm tra.

This is very natural too. In everyday speech, many learners hear không chỉ quite often.

Yes. The normal pattern is:

Subject + không những/không chỉ + part 1 + mà còn + part 2

In your sentence:

• Họ = subject
• không những cho ăn = first action
• mà còn kiểm tra = second action

The two parts should be parallel. Here, both are verb phrases:

• cho ăn
• kiểm tra

That parallel structure is one reason the sentence sounds natural.

Yes, in this sentence họ is the third-person plural pronoun they.

Do not confuse it with the noun họ meaning family name / surname in other contexts. Here, because it comes at the start of the sentence as the subject, it clearly means they.

It sounds natural and correct. However, không những ... mà còn ... can feel a little more structured or slightly formal than very casual speech.

In everyday conversation, many speakers might also say:

• Họ không chỉ cho ăn mà còn kiểm tra.

Both are good Vietnamese. The sentence you were given is standard and completely natural.