Hi, if you are not happy with the current cloud offerings that we provide you can easily host your own server instance of bitwarden. See here for more information https://help.bitwarden.com/article/install-on-premise/

Yes, the addon will offer to save new logins if it does not detect the current login in your vault. There are currently a few edge cases (one being on this website) that we are still working to resolve. For the most part it will offer to save.