All games are saved in the archive but only the last 30 days are available to basic members. Don't know if this is changing with v3 of the site or not.
When you click on the Completed Games header line in the app, is that where it is only showing 10 games?
I know in the current version of the site, being premium gives access to your full game archive.
In looking at the upgrade page for v3, it looks like basic members are listed at 10 games for the archive , but that may be wrong (or may change).
No. All games played on the site are stored in the archive and are accessible to premium members.
Can you look at all the games you have ever played on here? I play on the app, and it lists only the last 10 or so games I have played.