does exists a tool to monitor how many, and which files are changed day by day ? I would like to 'monitor' how many Mbyte /Gbyte of data changes in my company file server day by day for a 'remote' backup purpose.
Check out the File Server Resource Manager, it has some reporting capabilities that may give you what you are looking for. Worst case it can show you the last modified date for all files.
Most backup tools, once installed and running will of course only take incremental backups (or deltas) of what has changed. You can then monitor them to see what files are typically changing.