My dDaily rRoutine

Title capitalization rules

I staylive in thea dormitory.

We would use "stay" for short-term / temporary instances, such as a hotel or hostel. We use "live" for dormitories. Switched "the" to "a", since this dormitory hasn't previously been mentioned, you are introducing it in your story.

I leave the dormitory about 8-8.between 8 - 8:30 a.m.

You can use "at about" when you are fixating around one time. Example: "I leave the dorm at around 8:15 a.m." But since you are mentioning a time range, you should use "between"

I am an eEnglish prep student.

English is always capitalized

My school finishes at 12.:45 or 3.:30 p.m. (, depending on the day).

I would expect a little more information on why you list two different end times. Perhaps on certain days it ends earlier.

I feel very tired whenby the time my school finisheds.

This is a nuanced difference.

I feel very tired WHEN my school finishes => this could be interpreted as the moment your classes are done, you suddenly feel tired
I feel very tired BY THE TIME my school finishes => this means that over the duration of your classes, you become increasingly tired, and feel very tired by the end

After the school.,

I go toback to the dormitory.

You started your day at the dorm, so you are "going back" or "returning"

Firstly, I rest in my room.

Then I go downstairs forto have dinner.

Maybe I go out with my friends or stay in the dormitaory.

At the weekends, I usually seevisit new places because Izmir is a new city for me.

ItThis is my first (writing text / post) here.

These are most typically called "posts"

My dDaily rRoutine

titles are written in something called "title case," which has special capitalization rules

I leave the dormitory about 8-8.:30 a.m.

I am an eEnglish prep student.

My school finishes at 12.:45 or 3.:30 p.m.

I feel very tired when my school is finished.

"my" is not needed here

After the school., I go to the dormitory.

combined this with the next sentence for an improved flow and to fix the fragment "after the school"

you could also say "back to the dormitory" since you are returning there

I go to dormitory.

Then, I go downstairs for have dinner.

Maybe I go out with my friends or stay in the dormitaory.

AtOn the weekends, I usually see new places because Izmir is a new city for me.

It is my first time writing text here.

this sounds more natural