Transfer to different wallet and different network

Hi everyone,

I'm quite a noob with blockchain, i'm trying to achieve something but can't find this use case, so i thought i'll ask here.

Would it be possible to make a transfer from L1 wallet to L2 wallet through the bridge (and paying the gas fees only once)?

Is it possible to make a transfer between two L2 (different wallet) without paying L1 gas fees?

Thanks for your help.