The unattainable is unKNOWn at ZomboCom.

Disappearing icons is a bug with your launcher, nothing to do with the actual browser you’re using.

If you’re looking for a browser that was specifically designed for web apps, check out Hermit. (Disclaimer: I’m the author).

Thanks for the shout out for Hermit!

Did you mean “offline” as in not online (which makes little sense for a browser), or more like “not tied to a specific service that may hold your data hostage or infringe upon your privacy”?

If the latter, then I’ve found that a simple HTML file with manually added entries works great. I’ve set it as the home page in all my browsers. I retain full control over content and layout as well.)