Hey Francesco!

For logging in and signing events - If you want to use the extension in mobile, it's not possible.... yet! We are working on an extension to Firefox mobile.

For receiving zaps - yes, you should be able to set up your LN address in most mobile client

For sending zaps - depends on the client! Many already support #NWC ( nostr:npub142gywvjkq0dv6nupggyn2euhx4nduwc7yz5f24ah9rpmunr2s39se3xrj0, nostr:npub1gp4xzpmluelsakjtayc4wtzj97fhj5kakqjvsannu00xkdlf4x8s0xdqyq) and you can connect your Alby Account to enjoy your wallet on nostr!

let us know if that answers