I watchedhad a nightmare today.

However I actually got up 2 o'clock because ofit was too hot.

So I slept again at 4 o'clock after I did homework.

WatchingI had a nightmare is stared.

First I was in the middle of going to school.

CThe current season is summer, isn't it?

Here is not inThis isn't Australia.

I went toa little further, and there iswas a man who iws older than me.

He putted out into me suddenlysuddenly punched me.

putted out = punched? attacked?

I tried to check who is putted out intopunched me but I couldn't watch itsee because my eye was bad.

This is a part of dream though IIn this dream I had dropped my glasses.

So iI ask thated, ''aAren't you my school student?" However he doesidn't asked answer my question. I only knoew he wearas wearing light blue shirt.

I couldn't counterattack him because I was sick so I ruan away when he was heading towards the car.

I opened the door but I couldn't lock the door.

I had my mother lock thed door and I woke my father up and I told him that an intruder had come to my house.

My mother locked the door but we heard sounds thatfrom someone triedying to open the door.

I watchedhad a nightmare today.

Even though in Japanese we say "悪夢を見る", in English we say "have a nightmare".

Yesterday I went to bed at 9:30, and I triplanned to get up 4 o'clock.

(1) [動詞] + つもりだ: plan to (do something). Try to (do something): ～てみる.
(2) You can omit the second "I", because it "borrows" the subject from the first half of the sentence. It will sound more natural this way.
(3) You can add "pm" to clarify that it's night time: "9:30 pm".

However I actually got up at 2 o'clock because ofit was too hot.

So I went back to sleep at 4 o'clock after I did homework.

Your original sentence isn't grammatically wrong, but since you're returning to bed after waking up, I'd suggest the phrase "go back to sleep".

Watching nightmare is stThat was the start of my nightmared.

First I was in the middle of going to school.

CThe current season is summer, isn't it?

Alternatively: "It's currently summer, isn't it?"

HereThis is not in Australia.

The original sentence is awkward. I have corrected it so it sounds natural.

I went toforward a little further, and there iwas man who iwas older than me.

(1) Adding the "and" makes the sentence flow better.
(2) Mind the tense. You're writing in the past tense, so you should use "was".

He puttedshed me out into methe snow suddenly.

押し出す: push out.

I tried to checksee who is putted out into met was but I couldn't watch itsee because my eyesight was bad.

Again, mind the tense.

This iwas a part of the dream thoughwhere I dropped my glasses.

So iI ask thated, ''aAren't you my school student?mate?" However, he doesidn't asked answer my question. I only know he wearore a light blue shirt.

(1) 学校の人: schoolmate.
(2) 答える: answer.

I couldn't counterattack him because I was sick, so I ruan away when he was heading towards the car.

Added the comma so the sentence is easier to read.

I opened the door but I couldn't lock doorit.

(1) There's no need to repeat the subject "I" and object "door". The sentence will flow better this way.
(2) The transition is quite abrupt; it's not clear what door you're referring to. Perhaps it will be good to clarify this in your writing.

I had my mother lock thed door, and I woke my father up and I told him that intruder come my housethere was an intruder.

My mother locked the door but we heard the sounds that of someone triedying to open doorit.