Why did they say that one of their brothers is missing?
Rashi, Ramban (11), Ohr ha'Chayim: Yosef initially accused them of entering in 10 different gates and then meeting together - a sign that they were spies. They replied that they met together because they were brothers; they entered in ten different gates to look for their missing brother. 1
Ramban: And the Torah does not elaborate to provide us with all their arguments and counter-arguments.
How did the brothers try to prove that they are not spies?
Seforno, Ohr ha'Chayim: Seeing as their father lived in Kena'an, Yosef would be able to check with him and with his neighbors on everything that they had told him.
Malbim: A father would not send virtually all his sons to a place of danger. Our father had only 12 sons, and only one is with him now! Perhaps a king would risk his life and his sons' lives for his kingdom.
Ha'Emek Davar: We are from Eretz Kena'an, which is near Egypt. If the kings of Kena'ani wanted to fight e.g, they would not need to send spies to see Ervas ha'Aretz. Also, the Katan is there; you can check with him if anyone else is missing. Also, one brother is missing, and perhaps he is here. We would not fight here, lest we kill him!