Layer 2 adoption and segmentation problems. How is this solved?

I understand adoption of layer 2s is hoped to solve the gas problem. But I don’t understand how the eth ecosystem will solve the segmentation issue resulting from this.

If I have a an NFT on a layer 2 can I send it to another layer 2 or to layer 1? If I want to join a DAO formed on layer 1 can I do that from layer 2 (like Constitution DAO)? If I want to receive funds on one layer 2 from someone using a different layer 2 is that possible?

Thanks for your help.