Home Oor Aa Summer House

For titles, short conjunctions like "or" and short articles like "a" are not capitalised. A word is "short" if it has less than 3-4 letters (depending on the style guide you follow).

I live in Istanbul and everybody knows that Istanbul is the one of the most crowded cities in the Wworld.

"World" is not a proper noun here, so it should not be capitalised.

I have been living in the same exact area since my birth, it is called Tuzla and like aes at the border of Istanbul's east side.

Alternatively: "it is called Tuzla and lies at the border of Eastern Instanbul."

I really love this place beacause Tuzla is really so similar tolike a Hholiday place;destination: there isare not a lot of cars or traffic, everybody know each other who lives in the same place knows each other, almost every house ha have theirs its own pools… Just now I arrived at myreturned home from shopping.

(1) "Holiday place" is okay, but you can consider "holiday destination".
(2) The colon might be more appropriate than the semicolon here, since what follows behind is an explanation of why Tuzla is like a holiday destination. (One function of the colon is to indicate an explanation.)
(3) I think it's more natural-sounding to move "who lives in the same place" forward, so it's clearer that it's referring to "everybody", rather than "each other", if that makes sense.
(4) "Everybody" is singular, so "knows" is expected.
(5) "Every house" is singular, so the singular form of words should be used ("has", "its", pool").

I went'd gone to the market with wearing all blue clothes and with my cCrocs slippers while wearing myand sunglasses.

(1) You going to the market happened before you returning home. Since it's "the past of the past", the past perfect tense "had gone" should be used.
(2) "Crocs" is the name of a brand. Strictly speaking, it should be capitalised.
(3) Deleted some words from the second half of the sentence so that it's more concise and flows more nicely.

I only bought cold drinks and a fewsome ice creams for home while listetning to music inwith my earphones.

"Ice cream" is generally an uncountable noun. To make it countable, you can use counters: "tub of ice cream", "cup of ice cream", "box of ice cream", etc.

I felt like I was in a Ssummer house or a holiday place as if I havent been living in this plac'm just a tourist who doesn't live here.

I made some additions to the second half of the sentence so that it's clearer. Replaced "in this place" with "here" to avoid using the word "place" too much in close proximity.