Sometimes I sigh really loudly because I feel like I'm not getting enough air. Is this normal?

It's normal. We periodically "sigh"(take a deep breath, subconsciously) to expand our lungs and prevent alveolar collapse. It happens often when we're reading or engaging in a low physical stress exercise.
Yes. A natural reflex that your body often does without you being even conscious about it (similar to yawning), but sometimes you sigh voluntarily ... Someone once estimated average as two sighs per hour ...