joreopsigi kkeutnago naseo gajokgwa sajineul jjigeoyo.

Because 끝나다 means to end and is an intransitive verb. That means the thing that ends is treated as the subject, so it takes 이/가.

• 졸업식이 끝나다 = the graduation ceremony ends
• 졸업식을 끝내다 = to end/finish the graduation ceremony

So in this sentence, the ceremony is not being actively ended by someone; it is simply ending, which is why 졸업식이 is correct.

-고 나서 means after doing ..., with a clear sense that the first action happens first, and then the next action happens after that.

So:

• 끝나고 나서 = after it ends

It emphasizes sequence:

1. the graduation ceremony ends
2. then the speaker takes photos with family

This pattern is very common in Korean for showing one completed action followed by another.

It can feel repetitive from an English point of view, but in Korean -고 나서 is a fixed grammar pattern.

• 끝나고 by itself can mean and then it ends / after ending
• 끝나고 나서 more clearly stresses after it has ended

So it is not wrong or unnatural. In everyday Korean, -고 나서 is a very normal way to connect actions in order.

Yes. 졸업식이 끝난 후에 가족과 사진을 찍어요 is also natural.

The difference is mostly style and nuance:

• 끝나고 나서 sounds very natural and conversational
• 끝난 후에 can sound a bit more formal or written

Both mean essentially after the graduation ceremony ends.

Here 과 means with.

So:

• 가족과 사진을 찍어요 = take pictures with family

A learner may notice that 과/와 can also mean and, and that is true. But with a verb like 사진을 찍다, it is understood as with the person you are taking the picture with.

Also, 과 is often a bit more formal or written. In everyday speech, people often say:

• 가족하고
• 가족이랑

These all mean roughly the same thing here.

Korean uses 찍다 for taking a photo.

So:

• 사진을 찍다 = to take a photo / take pictures

Literally, 찍다 has meanings like to stamp, to mark, or to snap depending on context, but when used with 사진, it simply means to take a picture.

This is just the normal Korean expression, so it is best learned as a set:

• 사진을 찍다

Because 사진 is the object of the verb 찍다.

• 무엇을 찍어요? = What do you take a picture of?
• 사진을 찍어요 = take photos

So 을/를 marks the thing receiving the action.

Yes, 찍어요 is in the polite present-style form, but in Korean this form is often used for:

• present actions
• habitual actions
• planned or expected future actions

So depending on context, 찍어요 can mean:

• I take pictures
• I’m taking pictures
• I will take pictures

In this sentence, because of the time expression after the graduation ceremony ends, it can naturally refer to a future or planned action.

If someone wanted to make the future meaning more explicit, they could say:

• 사진을 찍을 거예요

But 찍어요 is still completely natural.

Korean often leaves out possessives like my, your, or our when they are obvious from context.

So 가족과 often naturally means:

• with my family
• sometimes with the family, depending on context

If the speaker wants to be more explicit, they could say:

• 제 가족과 = with my family
• 우리 가족과 = with my/our family

But very often Korean does not need that extra word.

Korean very often omits the subject when it is understood from context.

So this sentence could mean:

• I take pictures with my family
• I’m taking pictures with my family
• I’ll take pictures with my family
• in some contexts, even we take pictures with family

The listener usually understands who the subject is from the conversation or situation. This is extremely common in Korean and sounds more natural than constantly repeating pronouns.

찍어요 is the polite, everyday style, often called 해요체.

It is very common in normal conversation when speaking politely but not too formally.

Compare:

• 찍어요 = polite everyday
• 찍습니다 = more formal
• 찍어 = casual, plain speech

So this sentence sounds polite and natural for many everyday situations.

Korean often puts background information first and the main action later.

So the sentence structure is basically:

• After the graduation ceremony ends
  • take pictures with family

This is very natural in Korean. The earlier clause sets the scene, and the main action comes at the end. Since Korean verbs come at the end of clauses, this word order is very common and expected.