Sqlite on both Windows Phone 7.1 and Windows Phone 8
I have used sqlite in my app for windows phone 7 as described in the dotnetslackers link and its working fine in WP 8 ( I tested in WP8 emulator).
I don't see any point for saying "All Sqlite Clients for Windows Phone are out of date and not supported any more". Did you try yourself ?
Also this link says "SQLite is now supported on Windows RT, Windows 8 Metro Apps and will be supported on Windows Phone 8 for local application storage."
And here is one more link, which I didn't test.
I suggest you to try the dotnetslackers link and post here if you face any problem. Good luck !!
Note that SQL Server Compact 4.0 does not have a release for Windows Mobile, Windows Phone or for Windows CE devices. http://technet.microsoft.com/en-us/library/gg592946.aspx
You can use SQL Server Compact 3.5 on WP 7.5, but I'm not sure if this version works on WP8.