Thanks Katiss for this essay.

Your essay is 334 words, which is OK (there’s no point writing more than 350) and the average number of words per sentence is 17.8, which is a little high. Adding more short sentences will reduce this figure and increase impact. 

Introduction

Could the first sentence be left out?

You wrote:

Violent behavior in children and the rise of crime is often attributed to more violent games. In particular, violent computer games are frequently blamed for such behavior. In general, games are a safe way for children to explore concepts, such as violence, and they should be allowed to do so. There are more grave influences that should be the focus of crime prevention.

Here's a shorter version with the first two sentences combined:

Violent computer games are frequently blamed for aggressive behavior in children and for the rise of crime. In my opinion, however, games are a safe way for children to explore concepts such as violence, competition, and persistence. Crime prevention should focus on more important issues.

This sentence is very difficult to rewrite! However, we do need to change the word order and add 'be.' Let's also remove 'such as' since you have only one example ('violence'):

• Some concepts, such as violence, can safely and in a socially acceptable way explored in games but not in reality. →

Concepts such as violence can be explored safely and in a socially acceptable way in games.  OR

Violence is better explored safely in games than experienced in reality  OR

It's far better for children to explore violence in games than to experiment with it in reality. 

• age-adequate  → Age-specific

Your sentences are often correct but could be slightly shorter:

1. While playing them may serve as a relief of aggression less mental stable players may loose sight of reality spending too much time with them. (25). →
   While such games may relieve aggression, some less-mentally stable players may lose sight of reality after playing for too long. (20)
2. In this case playing  might for violence it might shift the boundaries for violence instead of teaching the players about what is acceptable. (23)→
   In this case playing might shift the boundaries of violence instead of teaching players about what is acceptable. (18)
3. If a child makes violent experiences, like being bullied or domestic violence in the family, it is more likely to turn violent itself. (23)  → 
   If children suffer/undergo/experience bullying, domestic violence or other forms of aggression, they are more likely to become violent themselves. (19)

These edits are just suggestions -  there is little or nothing wrong with your sentences. An easier way to reduce the average sentence length would be to add a couple of short sentences.

Here are some possibilities:

• Violence is all around us.
• Unfortunately, our children grow up in a violent world.
• Children have to learn that violence is not the only response.
• Games allow us to explore our dark side.
• Too much time spent on computer games is clearly unhealthy.
• Games should have age restrictions.
• Games fantasize and glamorize violence.
• Games teach a distorted view of violence.
• Games allow children to relieve natural frustrations safely.
• It’s easy to blame violent games for crime.