The correct answers are:
1: inspire 2: permeate
So the completed sentences would read:
"One by one, the students in the classroom next to the science lab began to look up and inspire deeply at first and then quickly cover their noses. Something was going terribly wrong in the science lab, and the smell was beginning to permeate the other classrooms on the hall."
- "Inspire" fits the context of taking a deep breath, while "permeate" means to spread throughout, which is appropriate for a smell.