If the horcruxes are shielded with Dark Magic and cannot be destroyed by common magic, why is the locket broken by the Sword of Godric Gryffindor?
The keyword is "common magic". The sword of Godric Gryffindor has the poison of the basilisk Harry killed in Harry Potter and the Chamber of Secrets. The basilisk's poison is one of the few ways to destroy a horcrux.
A horcrux is hard to destroy because it is the exact opposite of the human existence. While the death of a human leaves his soul intact (while his body is destroyed), a horcrux is an object that has part of the creator's soul. When you destroy a horcrux, the fragment that lies in there dies. That's the reason horcruxes are very hard to destroy. Of course, Voldemort had also placed a lot of powerful spells on his horcruxes to make them nearly impossible to destroy.
If Voldemort looks for the Elder Wand, why did he risk the stability of his soul and make six horcruxes to become immortal when he could just unite the three Deathly Hallows? Does he know of the existence of the Deathly Hallows?
In fact, Voldemort doesn't know the story (and thus the existence) of the Deathly Hallows. He doesn't even know about the Resurrection Stone, despite the fact that he had it in his possession in the form of Marvolo's Ring. He only knows the existence of the Elder Wand because of its bloodstained story (it became a legend as a wand that made its owner invincible, causing people to kill each other to take it). He wasn't told the "Tale of the Three Brothers" when he was a child; he was in a muggles' orphanage where such fairytales are unknown. So, he overlooks the existence of the Deathly Hallows and that's the reason he never tried to find and unite them to become immortal. He chose the brutal way, to murder and rip his soul; that is a reference to his inhuman nature.
What is the deal with that shard of mirror that Harry uses?
As previously mentioned, part of this story will be explained in Part 2. However, some explanation, which was omitted from the films, can be found in earlier books. Harry Potter and the Order of the Phoenix reveals that James Potter and Sirius Black were frequent trouble-makers at Hogwarts (not unlike Fred and George Weasley), and were often assigned detentions. When they were given separate detentions, each of them would keep his own mirror with him and use it to communicate with the other. When the magic about them is used, each mirror acts more like a window, allowing them to look through the other mirror into the face of whomever is holding it. At Christmas, Sirius gives one of these to Harry, telling him to use it should he ever need to contact him. Not wanting to lure Sirius into danger, Harry doesn't even open it and has quite forgotten it. After Sirius's death, however, he finds it again and opens it but then angrily destroys it. Nevertheless, Harry finds the mirror shard when cleaning out his trunk over summer, glimpses a blue eye, and decides to keep the mirror shard with him.