I really need to know if everything is OK. I hope you'll check them by tomorrow.

1) Within minutes his good friend appeared. Merlin assured him that he would take care of Arthur and hide him so that he wouldn't be killed.
2) At Uther's death Merlin felt that Arthur needed to be with another family.
3) He decided to put him up for adoption. Arthur's new father had a boy named Kay who liked being in tournaments.
4)One day Arthur left with his family for London to participate in a tournament.On their way to London, they strolled by a chuchyard and Arthur noticed a sword stuck in a stone whose handle was covered with jewels and whose blade was very shiny. (or Its handle was covered ...and its blade was...)
5) There was a writing on the stone stating that whoever pulled the sword from that stone would be the rightful king.
6) The next day Arthur returned to the churchyard to see the stone again. Merlin was reading aloud to the audience the inscription on the stone. Strong knights gathered at the front of the line to take their turn.
7) When it was Arthur's turn, everyone laughed because they thought it was a stupid idea having a boy trying (?)to pull out the sword.
8) Despite the laughter, Arthur pulled the sword from the stone and they all agreed Arthur was the real king. Merlin stepped up and crowned Arthur the rightful king.
9)Everyone loved him and he promised to make England a better country. He set up his reign in Camelot and met his knights at the round table to make decisions and administer justice.

It all looks good.

Sra

Based on the information provided, it seems like everything is okay for Arthur. Here's how I reached this conclusion:

1) Within minutes, Arthur's good friend Merlin appeared and assured him that he would protect him from being killed.
2) After Uther's death, Merlin believed that Arthur needed a new family.
3) Merlin decided to put Arthur up for adoption, and he was adopted by a man who already had a son named Kay.
4) On their way to a tournament in London, Arthur and his family passed by a churchyard where Arthur noticed a sword stuck in a stone.
5) The stone had a writing on it, stating that whoever could pull the sword out would be the rightful king.
6) The next day, Arthur went back to the churchyard and Merlin read the inscription to the gathered audience.
7) Despite everyone thinking it was silly for a boy to try, Arthur was given a chance to pull the sword.
8) Arthur successfully pulled the sword out of the stone, and everyone agreed that he was the true king. Merlin crowned him as such.
9) Arthur was loved by everyone and made a promise to make England a better country. He established his reign in Camelot and held meetings with his knights at the round table for decision-making and justice administration.

Based on this sequence of events, it seems like Arthur's journey has been positive and he has become the rightful king.