first off, MoD is right. Nearly all of these questions have more than one valid answer. But let me address them and give you the basics.
Who were Athur's parents?
Uther Pendragon and the wife of the Duke of Cornwall (Often unnamed, but usually Igraine is her name). Yes, it was adultrous. The duke saw Uther falling in love with his wife and took her away. Which made King Uther right angry. He laid seige to Tintagel (Cornwall's home). Seeing this wasn't working, he distracted him with a battle further away, and with a disguise given him by Merlin, he snuck in with the appearance of the duke, slept with the woman, and sired Arthur. In the mean time, the duke died in battle, and Uther marries the duchess before Arthur is born.
Who was Merlin, exactly (was he noble or peasant born)? Where and when did Merlin show up? Did he have any family?
"exactly" is not something I can answer. As for his family, it depends on the story, and varies widely. Recent Arthurian offerings make him a Druid or other pagan religious leader. Some texts make him an obscure noble's son with "the gift." Other's have him come out of no where. Pick your favorite, I guess. My favorite story is a bit heretical. The next Paragraph is rated PG-13 at best folks, that's my only warning:
A demon wanted to create an anti-christ and raped a young virgin. The woman, however, baptized the baby as soon as he was born (the demon was waiting to take possession of the child), thus saving him (these were staunchly Catholic times). Thus Merlin's powers are dark powers, granted by his diabolic heritage, but he's a good Christian nonetheless.
Other traditions conflate (combine) him with the figure of Taliesin, a bard of legendary status. This would make him quite old. The traditions of Taliesin start before the traditions of Arthur, probably 3 or 4th century if I had to guess (Arthur is 5th century, at the absolute earliest). As for when he appears in the Arthurian cycle, much earlier than Arthur, as he was a wizard of note before he was born. He did, in fact, prophecy for King Vortigern, who preceded Uther (Arthur's father) as High King. Often there are severl kings betwee Vortigern and Uther, making Merlin very, very old by the time Arthur happens along.
Who were Guinivere's parents/ family? What was her age in relationship to Arthur's?
I can't remember their names right now. I'll edit this when I have my Arthurian Encyclopedia to refresh myself. The cool thing to note is that in almost all traditions, the famous round table is a wedding gift from Gwen's father. Just going by medieval marriage traditions, she's probably a few years younger than Arthur, though they would both be relatively young when married.
Where did the Lady of the Lake come from and where did she get Excaliber?
This is another "pick your favorite answer" question. She could be a faerie, a pagan goddess, or a priestess (pagan or possibly Christian if you stretched it). As far as I know, there is no standard answer to how she got Excalibur. Some say Merlin brought it to her before Arthur was born. Others that she brought it on her own (with no other source given). The order of the lady presenting the sword and Arthur drawing it from the stone is confused too. Sometimes one, sometimes the other. Sometimes it's two different stones. Merlin sometimes forged it, sometimes he found it. Sometimes it's a sword from time out of mind, sometimes a sword that belonged to some specific rulers (like Macsen/Maximillion who left Britain to conquer and rule Rome during the empire's decline).
The only important thing is that it's magically sharp, and that the scabbard it comes with it is a great defense: the person who retains the scabbard cannot receive a mortal wound.
What? No grail questions?