Isaiah was married and had at least 2 sons. What wee their names?

Their names were Shearjashub and Maher-shalal-hashbaz. Though it is not mentioned in the Bible it is possible he had other sons and daughters.

Source: Isaiah 7:3 and 8:3

Isaiah was author of other non Biblical books. He wrote a Biography of a King of Judah. Which King was it?

It was King Uzziah. This book has been lost in history, no known copies exist.

Source: 2 Chronicles 26:22

During the reign of King Hezekiah Jerusalem was besieged. Isaiah prophesied that God would defend the city and he did. What country were the invaders from?

The invaders were from Assyria and led by Sennacherib. God sent an angel to smite the army.

Source: Isaiah 37

I was King of Judah Isaiah was my prophet. One time when I was sick Isaiah gave me a message from God that I would die. After praying to God I was granted extra life. Who am I?

I am Hezekiah King of Judah. As a devout Jew Isaiah and I had a good relationship.

Source: Isaiah 38 and many other mentions

When Isaiah was called by God he was concerned about his unclean lips. How did an angel clean them?

The angel used a hot coal from the fire. Needless to say, “Don’t try this at home.”

Source: Isaiah 6:7