On a warm, sunny morning, at six AM to be exact, I found myself in dark clothing at a funeral home.
This would be a good start if you were to elaborate on the funeral, but you don't. I think starting off with the shock of the phone call, or something along those lines, would be better.
I had not slept for twenty four hours and I felt all cried out
Using "I" twice in a sentence always looks awkward.
Of course, this assumption was proven wrong just minutes later.
I don't quite follow. What was proven wrong just minutes later? Sorry, it feels like I'm nitpicking at every sentence, but I promise it's mostly the beginning that needs massive reworking.
"He died, my dad is death".
my dad is dead
I started calling my mom and told her; she could not believe she refused to believe it.
Redundancy of "believe"; why are you saying the same thing twice?
The person took us to the movies, the beach, the arcade was gone.
The person who
took us to the movies..."
My grandpa's, or how we used to call him "Tata", death was a tragic
The death of my grandpa, or "Tata", as we used to call him, was tragic
... or something along those lines. It's one of the occasions where you have to weigh style against meaning.
At the beginning of the summer, I assumed I was the oldest daughter of both of my parents but then I discover I was never the oldest. I found out that my dad had had a daughter before he married my mom whom I had have not yet met.
Wow, wow, wow! We were talking about your grandpa, and now we're on to something this different. A bit abrupt, don't you think?
It's a good idea, but needs to be reworked to read better. To me, it looks like you wrote this in a real rush.