Update 09 November, 2023

Currently if you loose them and didn’t store them on the Network, you can’t recover them.

The Network does not store this information automatically as of now. On the other hand, a good wallet implementation in my opinion should backup those on the Network as you suggest, so you only have to keep your secret key (from which you can generate your MainPublicKey).

This would take a while to explain but to make it simple, the CNR contains a NetworkAddress and a secret DerivationIndex. With both this secret and the data found at the NetworkAddress (address of a SignedSpend), the owner can re-create the CN.

The size depends on the size of a Tx: cf here for a practical example.

Yes we can re-create CN from a CNR + secret key! Without the secret key the CNR is indeed useless.

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