Is the presence of the Mushaf in the kitchen, and my brother's saying, "Why is the Qur'an in the kitchen? Does it eat?" considered mockery of the religion, and is the laughter of those who heard it considered disbelief?

Mocking the Book of Allah the Almighty is an act of disbelief that expels one from the fold of Islam. What your brother said, and what those who laughed at it said, should not be interpreted as mockery, but rather as a sign of respect for the Mushaf (copy of the Quran) and a disapproval of leaving it in the kitchen. The sacred things of Allah and His Book must be revered, and the Mushaf should be placed in a suitable location befitting its status. It should not be left in the kitchen unless it is clean and in a safe place where there is no fear of contamination or disrespect.