L2 doesn't have to mean you leave the chain, it means you 'batch' transactions using this technique, generally : https://ethereum.org/developers/docs/scaling/optimistic-roll...

Not all L2 are about throughput exclusively, some are, for example, more focused on private ZKSnark based transactions. There is a huge quantity of development out there.

Generally the security guarantees on L2 range from identical to the main chain to 'good enough' to 'I pinkie promise not to take your money'. It's a permissionless protocol so that's kinda what you get.