Thank you very much Zobayda! It is my first steps in Farsi, so I am sorry for the terrible level!

No worries. I'm happy to help. I'll ask you if I don't understand something.

To avoid confusion, I rewrite your post in two different ways:

Spoken Persian: امروز همسايه ى من توی بازارِِ مركزِ شهر كار داشت. می‌خواست زود بیدار بشه.من توی ماشین در خونه‌ش منتظرش بودم چون اون ماشين نداره

Written Persian: امروز همسايه ى من در بازارِِ مركزِ شهر كار داشت. او می‌خواست زود بیدار شود.من در ماشین، جلوی در خانه‌ اش منتظرش بودم چون كه او ماشين ندارد

Wao amazing! Thank you again for the time spent! Now that you write both versions next each other, I notice that I already saw some elements of spoken Persian the last weeks (چون\ نداره).

Anytime! I try to write in spoken Persian from now on, so that you see them more frequently.