Neck pain from Armbars often occurs when you're not properly isolating the opponent's arm. Ensure your hips are driving into their shoulder joint, and your forearm is pressing against the bicep, not the elbow, while keeping your own head off the mat to avoid creating a leverage point for their defense.
To escape a larger opponent's Side Control, focus on creating frames with your forearms and biceps to prevent them from crushing you, then use your hips to shrimp your body away, creating space to establish a guard or get back to your knees. The key is to use your body's natural leverage and movement rather than trying to overpower them.
When facing a takedown, the most effective BJJ technique is to maintain a strong base by keeping your feet shoulder-width apart and your hips low, while actively circling your hips away from their pressure and using your hands to control their posture and prevent them from getting a deep grip on your body.