Thanks a lot for these questions! 

The Large Hadron Collider is indeed the accelerator localised at the French-Swiss border. Its third operation run started last July, so a couple of months ago. The reason of the previous shutdown (of a couple of years) was for upgrades in the machine and the detectors.

> I also know that it is a way to recreate small big bangs, my question is, have replicas of the big bang been created in laboratories? 

In its mode where heavy  nuclei are collided, the machine allows us to study the universe as it was a few moments after the Big Bang, and it thus allows us to understand this early history of our universe better. We do not recreate big bangs, but what is happening is more like a picture reproducing conditions that are close to those from the early moments of the universe.

> another question can these machines also produce black holes?

If you take certain theories as granted then yes. However, these theories also predict that those produced black holes quickly evaporate (in a few nanoseconds). For now, no black hole has been found in data.

I hope this answers  your question. Do not hesitate to come back to me if needed.

Cheers!