imouto ha watasi to onazi daigaku ni kayotte imasu.

In Japanese, family words are often used without saying my when it is clear that the speaker is talking about their own family.

So 妹 naturally means my younger sister in this kind of sentence.

A few useful points:

• 妹 = younger sister
• 姉 = older sister
• When talking about your own family to other people, plain forms like 妹 are normal
• When referring to someone else’s younger sister, 妹さん is very common

は marks 妹 as the topic of the sentence.

So the feeling is:

• As for my younger sister, she attends the same university as I do.

Using が would put more focus on who the subject is.
Using は is the more neutral, common choice when you are simply talking about your sister and saying something about her.

Here, と marks the thing or person being used for comparison.

The pattern is:

• A と 同じ = the same as A

So:

• 私と同じ大学 = the same university as me
• more naturally in English: the same university that I attend

This と is not the and meaning of と. It is the comparison use.

Because this is not a possession pattern.

• 私の means my
• 私と同じ means the same as me

So the sentence is not saying my same university.
It is saying a university that is the same as the one I go to.

That is why と is used, not の.

同じ is a slightly special word. It behaves somewhat like a na-adjective, but it does not behave exactly like a regular one.

Before a noun, 同じ usually comes directly before it:

• 同じ大学
• 同じ人
• 同じ場所

So 同じな大学 would sound wrong.

At the end of a sentence, you can say:

• 同じです
• 同じだ

So the important thing to remember is:

• before a noun: 同じ + noun
• not 同じな + noun

Because in Japanese, modifiers come before the noun they modify.

Here:

• 私と同じ modifies 大学
• so together: 私と同じ大学

A literal breakdown is something like:

• my younger sister / topic / same as me / university / to / attends

Japanese often puts descriptive information before the noun, where English often puts it after:

• Japanese: 私と同じ大学
• English: the same university as me

The verb 通う normally takes に for the place someone regularly goes to.

So you learn it as a set:

• 学校に通う
• 大学に通う
• 病院に通う

Why not を?

• を usually marks a direct object
• 通う does not treat the school as a direct object in this meaning

Why not へ?

• へ emphasizes direction
• with 通う, に is the standard and most natural choice

So 大学に通う is the normal pattern.

Because 通う means to go somewhere regularly, such as to school, work, or a hospital.

Compare:

• 大学に行く = go to the university
• 大学に通う = attend the university / commute there regularly

So if someone is a student at that university, 通う is the natural verb.

Yes, it is 通う in the ている form:

• 通う
• 通っている
• polite: 通っています

But with 通う, ている usually shows a habitual, ongoing activity, not an action happening at this exact moment.

So here it means:

• she attends
• she goes to regularly
• she is attending

It usually does not mean that she is physically on her way there right now.

通う is a u-verb.

For many u-verbs ending in う, つ, る, the て-form changes to って.

So:

• 通う → 通って
• 待つ → 待って
• 取る → 取って

Then you add いる:

• 通っている

And in polite form:

• 通っています

So the sentence contains:

• 通う → 通っている → 通っています

Sometimes yes, but only if the comparison is already clear from context.

In this sentence, 同じ needs a reference point.
Same as whom?

• 妹は私と同じ大学に通っています。 = clear
• 妹は同じ大学に通っています。 = possible only if the listener already knows what same university refers to

Without context, leaving out 私 can make the sentence feel incomplete or vague.

A natural reading is:

いもうと は わたし と おなじ だいがく に かよって います。

Word by word:

• 妹 = いもうと
• は = は (pronounced わ as a particle)
• 私 = わたし
• と = と
• 同じ = おなじ
• 大学 = だいがく
• に = に
• 通って = かよって
• います = います