Your English is fantastic! There are no real mistakes, just some suggestions to use a better synonym or improve the style. Your English sounds very natural -- to be honest, you could use a bit more Latin and less Anglo-Saxon to discuss such a serious subject.

Peace talks with FARC rebel group

Two negotiation teams, the first, ("from" or "representing") Colombia's Government, and the other, the FARC guerrilla group, are handling peace talks in La Havana, capital city of Cuba, looking (or aiming) for the end of fifty years of violence. These peace talks started two years and a half (more typically "two and a half years" like in the TV show "Two and a Half Men") ago and regardless of the long time that has already passed, there is not a definetely accord between the parties yet . In fact, the FARC guerrillas have done (or "carried out" or "committed") several violent attacks and instead of focusing their efforts to conclude the negotiations, they keep on hurting this country. If they were willing to make a real change as much as the Government and Colombian people are, they would start with an actual ceasefire. We hope that the teams eventually make a peace deal in search of (or "leading to" or "ushering in" a new era for Colombia.