Lost data, how to recover (sql server)
As long as your recovery model is Simple and full backups for only last 7 days you do not have any chance to see what was deleted in June.

Entries in the log file for Simple recovery are discarded when SQL Server does not need them for crash recovery.

The answer to your second question - yes, you have to switch to Full recovery. Then with the help of Apex software (or some other) you probably will be able to restore deleted in the past records if you have log backups for that period of time.
Be careful when switching to Full recovery - it has gotchas. Make sure to learn this Q/A.