jinryoreul gidarineun dongan hwanjadeuri joyonghi anja isseosseo.

Because 기다리다 normally takes the thing being waited for as a direct object, marked with 을/를.

• 진료를 기다리다 = to wait for medical treatment / a consultation
• So 진료를 is the object of 기다리는

Using 진료가 기다리는 would mean something like the treatment is waiting, which does not fit here.

A small note: in real-life Korean, 진료 can refer to medical treatment, consultation, or seeing the doctor, depending on context.

동안 means during or while.

So:

• 기다리는 = waiting
• 동안 = during / while

Together, 기다리는 동안 means while waiting or during the time when they were waiting.

This structure is very common:

• 먹는 동안 = while eating
• 공부하는 동안 = while studying
• 자는 동안 = while sleeping

In this sentence, 진료를 기다리는 동안 gives the time background for the main action.

기다리는 is the present modifier form of the verb 기다리다. When a verb modifies a noun like 동안, Korean often uses this form to mean the time during which someone is doing X.

So:

• 기다리는 동안 = during the time of waiting / while waiting

Why not the others?

• 기다렸던 동안 sounds unnatural here because it adds a completed or retrospective feeling that is not needed
• 기다리며 means while waiting, but it connects directly to another verb and would create a different sentence structure

For example:

• 진료를 기다리며 환자들이 조용히 앉아 있었어 is possible
• But 기다리는 동안 is more explicit and very natural

환자들이 means the patients and is marked with 이/가, the subject marker.

So the basic structure is:

• 진료를 기다리는 동안 = while waiting for treatment
• 환자들이 = the patients
• 조용히 앉아 있었어 = were sitting quietly

So 환자들이 is the subject of 앉아 있었어.

Both are possible, but they feel slightly different.

• 환자들이 uses the subject marker 이/가
• 환자들은 uses the topic marker 은/는

In this sentence, 환자들이 sounds like a straightforward description of what the patients were doing.

• 환자들이 조용히 앉아 있었어 = The patients were sitting quietly

If you said 환자들은, it might sound more like you are setting up the patients as a topic, possibly with contrast:

• 환자들은 조용히 앉아 있었어 = As for the patients, they were sitting quietly

So 이/가 is natural when simply presenting the subject of the action.

Not always, but it is natural here.

환자 can already refer to patients in a general sense, because Korean does not always have to mark plural. But 들 makes the plurality explicit.

• 환자가 = patient / patients, depending on context
• 환자들이 = patients

In this sentence, using 들 helps clearly show that multiple patients were sitting there.

So:

• 환자들이 조용히 앉아 있었어 = clearly plural
• 환자가 조용히 앉아 있었어 = probably one patient
• 환자가 조용히 앉아 있었어 could sometimes be interpreted from context, but usually singular

조용히 is an adverb meaning quietly.

It comes from the adjective 조용하다 meaning to be quiet.

To turn many Korean descriptive words into adverbs, you often use -히 or -게.

Here:

• 조용하다 = to be quiet
• 조용히 = quietly

It modifies 앉아 있었어, telling us how the patients were sitting.

So:

• 조용히 앉아 있었어 = were sitting quietly

This is a very important Korean pattern.

• 앉았어 = sat down
• 앉아 있었어 = was sitting / had been sitting

The verb 앉다 means to sit down, which is a change of state.
When Korean wants to express the resulting state, it often uses:

• 앉아 있다 = to be sitting
• Past: 앉아 있었어 = was sitting

So in this sentence, the patients were not just performing the action of sitting down once. They were already in the seated state for a period of time.

That is why 앉아 있었어 is the natural choice.

Korean often distinguishes between:

1. the action of changing into a position
2. the state after that change

With posture verbs:

• 앉다 = sit down
• 앉아 있다 = be sitting

Similarly:

• 서다 = stand up

• 서 있다 = be standing

• 눕다 = lie down
• 누워 있다 = be lying down

So 앉아 있었어 literally contains sit + be, but naturally it means was sitting.

This is different from English, where sit can sometimes cover both ideas.

있었어 is in the casual, informal speech level, often called 반말.

It would be used with:

• close friends
• younger people
• children
• people you are very familiar with

A more polite version would be:

• 진료를 기다리는 동안 환자들이 조용히 앉아 있었어요.

So the sentence you were given is casual/informal in tone.

Yes. Korean word order is flexible as long as the grammatical markers stay clear.

For example, these are all possible:

• 진료를 기다리는 동안 환자들이 조용히 앉아 있었어.
• 환자들이 진료를 기다리는 동안 조용히 앉아 있었어.

Both are natural. The difference is mostly about focus and flow.

Korean often places time expressions early in the sentence, so the original version sounds very natural.

Yes, often you can.

• 기다리는 동안
• 기다리는 동안에

Both mean while waiting or during the waiting period.

The 에 can make it feel a little more explicit, but in many everyday sentences it is omitted.
So the version without 에 is completely natural and common.

Yes, that is the most natural interpretation here.

In 진료를 기다리는 동안, the subject is not separately stated, but we understand that it is the patients who are waiting.

So the full idea is:

• 환자들이 진료를 기다리는 동안, 환자들이 조용히 앉아 있었어

Korean often omits repeated subjects when they are clear from context.
That is why the sentence sounds natural and not repetitive.