Firecracker

Last June two teenagers let off a big firecracker (which measures 5,9 x 2 which measured 5.9 x 2 {also: measuring 5.9 x 2} inches) at the playground, near children who are were {in the past} 5 years old.
I was in my office when the firecracker exploded. The walls were shaking.
My immediate reaction was to bend down.
I decided to demarcate a secure area and call the police.
I took the initiative to view the security cameras.
The next day the headquarter {meaning? the head office?}  complained to the gendarmerie police.
The children had trouble to get over getting over it, and many of them had a nightmare {more common: had nightmares}.

I hope that the police will catch up with and make an arrest them will catch and arrest them.

Firecracker

Last June (Was this last month, or last year? This wording sounds like it was last year, so if it was recently, I would say "Last month" instead), two teenagers let off a big firecracker (which measured 5.9 x 2 inches) at the playground, near children who are 5 years old. ("5-year-old children" or "young children" would sound more natural) 
I was in my office when the firecracker exploded. The walls were shaking.
My immediate reaction was to bend down. (You could also say "crouch down" or "duck for cover" to give the sense that you were protecting yourself — "bend down" is what you might say if you dropped your pen on the floor.)
I decided to demarcate a secure area ("I decided to secure the area" is a common way to describe that) and call the police.
I took the initiative to view security cameras.
The next day, the headquarters complained to the gendarmerie.
Children had trouble to getting over it, and many of them had a nightmares.

I hope that the police will catch up with them and make an arrest. them ("make an arrest" or "arrest them" are both correct, but not "make an arrest them")

This is a good text! There were very few errors, so I just made suggestions for ways to make it sound more natural.