wǒ gěi tā dǎ diànhuà de shíhou, tā zhèngzài kàn yīshēng xiě de chǔfāng.

In this sentence, 给 marks the recipient/target of the action.

So:

• 我给她打电话 = I call her / I make a phone call to her

It does not literally mean give here, even though 给 often means to give.

A very common pattern is:

• 给 + person + verb

especially with actions directed toward someone, such as calling, writing, sending, explaining, etc.

You can also say:

• 我打电话给她

That means the same thing. Both word orders are common.

打电话 is a fixed expression meaning to make a phone call / to call someone.

Even though 打 often means to hit, in Chinese it also appears in many set verb-object expressions where it has a broader, less literal meaning.

For example:

• 打电话 = make a phone call
• 打字 = type
• 打伞 = hold an umbrella
• 打球 = play ball

So in 打电话, you should learn the whole phrase as one unit rather than trying to translate 打 by itself literally.

的时候 means when, at the time when, or sometimes while.

It turns the clause before it into a time expression.

So:

• 我给她打电话的时候 = when I called her / when I was calling her

Basic pattern:

• [clause] + 的时候
• when [clause happens]

Examples:

• 我吃饭的时候，他来了。
  When I was eating, he came.

• 小时候
  when (someone was) little / in childhood

In your sentence, this whole first part sets the time background for what happened next.

It can often cover both ideas, depending on context.

Chinese does not always force the same kind of tense distinction that English does. So:

• 我给她打电话的时候 can mean
  when I called her
• or
  while I was calling her

In this sentence, the second clause has 正在, which strongly suggests an ongoing action:

• 她正在看... = she was in the middle of looking at...

So the whole sentence naturally feels like:

• When I called her, she was looking at...
• or
• While I was calling her, she was looking at...

English will choose one version, but the Chinese structure itself is flexible.

正在 shows that an action is in progress right at that moment.

So:

• 她正在看... = she was in the middle of looking at / reading...

It is similar to the English be + -ing idea, but it is specifically marking an ongoing action.

Compare:

• 她看处方。 = She reads / looked at the prescription.
• 她在看处方。 = She is looking at the prescription.
• 她正在看处方。 = She is right in the middle of looking at the prescription.

So 正在 helps show that at the time I called, her action was ongoing.

Both can describe an ongoing action, but 正在 is usually a bit more explicit or emphatic.

• 在看 = is looking / reading
• 正在看 = is currently, right now, in the process of looking / reading

In many everyday sentences, they are very close:

• 她在看书。
• 她正在看书。

Both mean She is reading a book, but 正在 can sound slightly more focused on the action being in progress at that exact moment.

In your sentence, 正在 fits well because the speaker is describing what she was doing at the moment of the phone call.

This 的 links a modifying phrase to a noun.

• 医生写的处方 = the prescription that the doctor wrote

The part before 的 is describing the noun after it.

Structure:

• [modifier] + 的 + noun

Here:

• 医生写的 = written by the doctor
• 处方 = prescription

So together:

• 医生写的处方 = the prescription written by the doctor

This is one of the most important sentence patterns in Chinese. It works like a relative clause in English.

More examples:

• 我买的书 = the book that I bought
• 他做的饭 = the meal that he made
• 老师说的话 = the words that the teacher said

Because in Chinese, modifiers normally come before the noun they describe.

English often puts this kind of information after the noun:

• the prescription that the doctor wrote

Chinese puts the whole descriptive part first:

• 医生写的处方

So the order is:

• doctor wrote + 的 + prescription

not:

• prescription + that the doctor wrote

This is a major difference from English. Chinese relative clauses come before the noun.

In this sentence, it means:

• look at / read the prescription written by the doctor

The reason is the grouping:

• 医生写的处方 is one noun phrase
• it means the prescription that the doctor wrote

So 看 is taking that whole phrase as its object:

• 看 [医生写的处方]

If you wanted to say watch the doctor write a prescription, you would usually say something like:

• 看医生写处方
• 看着医生写处方

Notice there is no 的 there. Without 的, the meaning can be about watching the action happen. With 的, it turns into a modifier for the noun 处方.

So 的 is doing important work here.

Here, 看 means something like look at or read/examine.

Because the object is:

• 医生写的处方 = the prescription written by the doctor

So:

• 她正在看医生写的处方
  = She was looking at / reading the prescription written by the doctor

This is not the same as 看医生 meaning to see a doctor.

That can be confusing, because:

• 看医生 = see a doctor
• 看医生写的处方 = look at the prescription written by the doctor

The phrase after 看 is longer, and the 的 tells you that 医生写的 is modifying 处方.

Because this sentence is focusing on time background and an ongoing situation, not on marking completed actions with 了.

First clause

• 我给她打电话的时候 sets the time: when I called her / when I was calling her

You do not need 了 here. The clause is just establishing the moment.

Second clause

• 她正在看... already shows an ongoing action
• using 了 with 正在 would usually be wrong in this kind of sentence

So the sentence naturally uses:

• no 了 in the time clause
• 正在 for the action in progress

Chinese often leaves aspect unmarked when the context already makes the timing clear.

Yes, often you can.

So:

• 我给她打电话的时候，她正在看医生写的处方。
• 我给她打电话时，她正在看医生写的处方。

Both are correct.

The difference is mostly style:

• 的时候 is more common in everyday spoken Chinese
• 时 is shorter and can sound a bit more written or formal

For learners, 的时候 is usually the safer everyday choice.

In many contexts, yes.

Both are understandable:

• 医生写的处方 = the prescription the doctor wrote
• 医生开的处方 = the prescription the doctor prescribed/issued

But 开处方 is a very common collocation for doctors, so 医生开的处方 often sounds especially natural.

Still, 写的 is not wrong. It simply highlights the fact that the doctor wrote it.

So the sentence is grammatical as given, but native speakers may often prefer:

• 她正在看医生开的处方。

The structure is:

• [time clause] ， [main clause]

Specifically:

• 我给她打电话的时候 = time clause
• 她正在看医生写的处方 = main clause

So the sentence means:

• At the time when I called her, she was looking at the prescription written by the doctor.

This kind of structure is very common in Chinese:

• 我回家的时候，他在做饭。
  When I got home, he was cooking.

• 老师说话的时候，学生都很安静。
  When the teacher was speaking, the students were all quiet.

It is a very useful pattern for describing two actions happening around the same time.