Like title says, is it possible to connect to SSAS without any of the AD or windows accounts? Can I store users credentials e.g. on my own SQL Server database or do I still need only AD? Because i think it is possible in SSRS with custom authentication (or I am wrong).
Windows authentication is only option, however you can login from remote machine this way:
Prepare on remote machine user account with exactly same login and password as user from ssas machine (with proper ssas access set) and you should be able to login using this user.
Or opposite: create on ssas machine user account with execly name and password as remote user and give him access to ssas.