Ramadan? I don't get the punishment for acts need to the capital death?

I have read the Quran and reading something in internet about adultery is also condemned by capital death and ual acts.. but I don't find anything in the Quran about the death capital for those punishments can you clarifiy me? if Allah is merciful why does He want to kill the sinners and not to give them a second chance? also for the thief the amputation is allowed.. where is Allah the most merciful? why is that? I have seen terrible images of people in islamic punishing in public for different crimes like stealing.. they have to be cut their hands. why is that?