Yes, trades are settled onchain.

Too expensive for who? 0x protocol allows you trade digital assets with anyone in the world, trustlessly, through the internet, for $0.10-$0.25 per trade. While this isn't perfect for all use cases, it is an incredibly powerful capability.

Scaling is indeed a limitation for decentralized networks. You can learn more about our scaling R&D efforts here: https://blog.0xproject.com/0x-roadmap-2019-part-2-scalabilit...