1)
What is the significance of touching the coal to his mouth?
1.
Radak: This removed the sin with a scald. From now and onwards, Yeshayah may talk.
2.
Radak citing Targum Yonasan: This is a metaphor. He arranged in my mouth words of prophecy. Malbim - this is like "Nasati Devarai b'Ficha" (Yirmeyah 1:9).
2)
For what sin did Yeshayah need atonement?
1.
Radak citing Yevamos 49b: He reviled Yisrael, and said "I dwell among a nation of Tamei lips" (5).
2.
Malbim: "I am a man of Tamei lips" (5), i.e. he refrained from rebuking. The Kaparah is via touching the coal to his mouth, i.e. he will be Hashem's Shali'ach for Nevu'ah and rebuke.