This explains the flex part: X30 Exhaust Notes — Fox + Son Karting
“Changes to the exhaust length are made by using different sizes of flexible steel pipe (referred to as “flex”) between the header and the actual pipe. A longer exhaust length gives you better bottom end power and a shorter length gives you more top end. Changing your exhaust length is akin to changing your gearing.”
Exhaust manifold:
What an exhaust manifold does:
https://www.brodiestireandautomotive.com/Auto-Repair/Automotive-Q-A/mode/detail/KnowledgeItemId/2669
One piece vs 2 piece exhaust thread: