How to determine if the SQL Server running is Express version?
You can execute SELECT @@VERSION. Result will describe SQL Server version and edition. Or SELECT SERVERPROPERTY('Edition') will result SQL Server edition.

SQL Server Express Edition supports maximum database size 10GB per database. So you can monitor database size using following query.

SELECT      sys.databases.name,  
            CONVERT(VARCHAR,SUM(size)*8/1024)+' MB' AS [Total disk space]  
FROM        sys.databases   
JOIN        sys.master_files  
ON          sys.databases.database_id=sys.master_files.database_id  
GROUP BY    sys.databases.name  
ORDER BY    (SUM(size)*8/1024) DESC


Thanks!