/* Total rows in a database */
SELECT SUM(TABLE_ROWS)
FROM INFORMATION_SCHEMA.TABLES
WHERE TABLE_SCHEMA = '{your_db}';

/* Size of all databases in MB */
SELECT table_schema "Data Base Name",
sum( data_length + index_length ) / 1024 /
1024 "Data Base Size in MB",
sum( data_free )/ 1024 / 1024 "Free Space in MB"
FROM information_schema.TABLES
GROUP BY table_schema ;