Apple provides a plug-in for Chrome to allow use of your stored passwords on Windows. Announced last year. I've tried it on Windows, appears to work, but do not know how secure it is.

--- Edited to remove references to Linux. Appears to be Windows only.

Yes. But you can't even use those password on Mac when you are using Firefox or Chrome.

It seemed quite buggy when I tried it.

Given Apple's track record with other web-related services on non-Apple platforms, don't expect it to improve much or at all.