The prince's sister has the title of "princess".
In 1857 Prince Albert was given the title of Prince Consort.
The title given to Prince Arthur was, " The Duke of Connaught"
If the father (Prince) does not hold another title, his children will be Prince or Princess. The off spring of that Prince will also be a Prince, but not so with the Princess - especially if she marries.
What 'is' Price Charles's royal title surely you mean, and the Prince of Wales
He is the "Crown Prince" of the United Kingdom so he has the title "His Royal Highness The Prince of Wales" and in Scotland he is known as "The Duke of Rothesay".
He will still be Prince William.
The title of prince or princess is granted by the reigning monarch, and indeed, Prince Edward's heir, James, has been granted the title Prince James of Wessex.
No. That title has been given to his father, Prince Charles.
He is the "Crown Prince" of the United Kingdom so he has the title "His Royal Highness The Prince of Wales" and in Scotland he is known as "The Duke of Rothesay".
Prince William has not lost his title as prince. The duke of york still retains his title as prince Andrew however it is common for the queen to give other titles to royal members when they marry. When William married Catherine she automatically receives the title princess William but they will be officially known as the duke and duchess of Cambridge. Also a duke is higher than a prince.
The suggestion is that the title was like the Prince of Wales: it was the title of the heir apparent.