Mẹ tôi sốt, vì vậy tôi mua thuốc cho mẹ.

Vietnamese often leaves out the verb to be when talking about states or conditions.

So:

• Mẹ tôi sốt = My mother has a fever / My mother is feverish
• Literally, it is closer to Mother my fever

This is very normal in Vietnamese. You do not need a separate word for is here.

Sốt means to have a fever or feverish.

In this sentence, Mẹ tôi sốt means your mother is ill with a fever. In everyday Vietnamese, sốt can function almost like a verb or condition word, so you can say it directly without adding extra words.

Vietnamese noun phrases usually go:

• noun + possessor

So:

• mẹ tôi = my mother
• nhà tôi = my house
• bạn tôi = my friend

This is different from English, where the possessor usually comes first.

Vietnamese often repeats subjects more explicitly than English.

So:

• Mẹ tôi sốt, vì vậy tôi mua thuốc cho mẹ.

keeps the second clause clear by stating tôi again: so I bought medicine for my mother.

In English, we also usually repeat the subject after so:

• My mother had a fever, so I bought medicine for her.

So this repetition is completely natural.

Vì vậy means therefore, so, or because of that.

It connects the first clause to the result in the second clause:

• Mẹ tôi sốt = cause
• vì vậy tôi mua thuốc cho mẹ = result

It is a bit more formal or written than plain nên in some situations.

For example:

• Trời mưa, vì vậy tôi ở nhà.
  It rained, so I stayed home.

Yes, very often.

A very common alternative is:

• Mẹ tôi sốt, nên tôi mua thuốc cho mẹ.

This also means My mother had a fever, so I bought medicine for her.

Roughly speaking:

• nên is very common in speech
• vì vậy can sound slightly more formal or more explicitly like therefore / as a result

Both are correct here.

Here, cho means for.

So:

• mua thuốc = buy medicine
• mua thuốc cho mẹ = buy medicine for mother

This is a very common pattern:

• làm cho tôi = do something for me
• mua quà cho bạn = buy a gift for a friend
• nấu ăn cho con = cook for the child

So cho marks the beneficiary, the person who receives the benefit of the action.

Because once mẹ tôi has already been introduced, Vietnamese often shortens it to just mẹ if the meaning is still clear.

So:

• Mẹ tôi sốt, vì vậy tôi mua thuốc cho mẹ.

is natural and means:

• My mother had a fever, so I bought medicine for her.

Saying cho mẹ tôi is also possible, but it can sound a little more repetitive in this context.

Yes, functionally it works that way in this sentence.

English usually uses a pronoun:

• I bought medicine for her

Vietnamese often repeats the relationship noun instead:

• tôi mua thuốc cho mẹ
  literally: I bought medicine for mother

This is very common and natural in Vietnamese. Instead of switching to a pronoun like her, Vietnamese often keeps the kinship term.

Yes. Thuốc is a general word for medicine, drug, or remedy, depending on context.

In this sentence, because the mother has a fever, thuốc clearly means medicine.

Some useful related expressions:

• thuốc cảm = cold medicine
• thuốc sốt = fever medicine
• uống thuốc = take medicine

Vietnamese often does not mark tense explicitly. The time is understood from context.

So:

• tôi mua thuốc can mean I buy medicine, I bought medicine, or I will buy medicine, depending on context.

In your sentence, the natural interpretation is past:

• My mother had a fever, so I bought medicine for her

If you wanted to make past time clearer, you could add đã:

• Mẹ tôi sốt, vì vậy tôi đã mua thuốc cho mẹ.

That more explicitly means I bought / I have bought medicine for my mother.

Yes, you can.

• Mẹ tôi sốt = My mother has a fever
• Mẹ tôi bị sốt = My mother got/has a fever

Adding bị can make it sound a bit more like being affected by an illness or condition. But in everyday Vietnamese, Mẹ tôi sốt is already very natural and complete.

Yes, it is grammatical and natural.

That said, in casual speech, many speakers might prefer:

• Mẹ tôi sốt nên tôi mua thuốc cho mẹ.

This sounds a little more conversational.

Your original sentence with vì vậy is still correct and natural, especially in slightly more careful or written-style Vietnamese.