How do i know a table size and row counts for each month, for the past six months? Using sql server can i get the row count and size of the table as well as the database size for the past six months?
Unless you are tracking tables, table size can not be known. To get current size:   

sp_spaceused 'TableName'


To get row count:  

Select count(*) from 'TableName'


To get row count with a timestamp field:   

    Select
          DATEPART(YEAR, 'timestamp_field') AS 'Year',
          DATEPART(MONTH, 'timestamp_field') AS 'Month',
          DATEPART(DAY, 'timestamp_field') AS 'Day',
          COUNT(*) AS Check

    from
         'TableName'
    group by
         DATEPART(DAY, 'timestamp_field'),
          DATEPART(MONTH, 'timestamp_field'),
          DATEPART(YEAR, 'timestamp_field')  
ORDER BY  'Year',  
          'Month',  
          'Day'


Database growth:  

SELECT
[database_name] AS DB,
DATEPART(day,[backup_start_date]) AS Day,
DATEPART(month,[backup_start_date]) AS Month,
DATEPART(year,[backup_start_date]) AS Year,
AVG([backup_size]/1024/1024) AS "Backup Size MB",
AVG([compressed_backup_size]/1024/1024) AS "Compressed Backup Size MB",
AVG([backup_size]/[compressed_backup_size]) AS "Compression Ratio"
FROM msdb.dbo.backupset
WHERE [database_name] = N'AdventureWorks'
AND [type] = 'D'
GROUP BY [database_name],DATEPART(m,[backup_start_date]),DATEPART(d,[backup_start_date]),DATEPART(y,[backup_start_date]),backup_start_date;  


for database size details. Check this link
Create table size tracking report