Yes. He was Henry's son with Jane Seymour (who died as a result of the birth.) The boy became king Edward VI. (King Henry had at least one other son, who was illegitimate, with Mary Boleyn, sister of Henry's queen, Ann Boleyn)
Yes, 1 son and 2 daughters. His only sons name was Edward and took the throne at the tender age of 9 when Henry VIII died. Edward VI ruled for 6 years before dieing at only 16 years old. Edward VI was a sickly child and the country was ruled by his protectors the Dukes of Somerset and Northumberland.
Henry VIII did not have a son. This was the primary reason he sought to divorce his wives. Indirectly, his inability to father a male child led to the English Reformation, as he split the English church from Rome so that he could divorce.