Unfortunately, burglaries related to the corruption are the most common crimes in Spain. In fact, they are often mentioned in the news. I can hear many about cases everyday in the media. And most of them, are committed by politicians or well-known businessmen. Corruption can be active or passive bribery, through fraud against an administration, illegal business and activities or abuse in public office. But the worst thing is, there is a certain sense of impunity about it, because most of the robbers won't go to the jail or give back the money. And people are really irritated. 

I think there should be more investigations and more serious punishment. (for those involved)
It is probably this corruption which gives us a very bad image abroad.

I'm not sure that you mean "burglaries". A burglary is when someone goes into a house or building and steals something from the property owner. A better fit would be theft or embezzlement (malversación)

Unfortunately crimes related to..........................
Unfortunately theft related to.......................
Unfortunately fraud related to........................

We wouldn't use the word 'robbers' we'd say something like:

"because most of those involved........."

"because those involved in stealing / misappropriating funds......................"

Finally, I'm not sure on the grammar behind it, but we don't start sentences with "And" probably because it is a continuation of a sentence)

Everyday in the media (television, radio, printed press)

Everyday on social media. (youtube, twitter, yahoo news etc)

Unfortunately, burglaries related to the corruption are the most common crimes in Spain. In fact, there are plenty of these stories in the news. I can hear many cases everyday on the media. And most of them are committed by politicians or well-known businessmen. The corruption can be active and passive bribery, through fraud against the administration, illegal business and activities or abuse of public office. But the worst thing is, there is a certain sense of impunity about it, because most of the robbers won't go to the jail and give back the money. And people are really irritated. 

I think there should be more investigations and more serious punishment.

It is probably that the corruption that makes us to have a very bad image abroad.