iTunes will perform a complete backup of the iPhone when it is plugged in for sync, which will contain all the application-specific data files. However, the only way to restore this is to restore the entire system image, so that is only an emergency backup, not what you need.
Third parties have typically provided their own backup and synchronisation strategies. There are two broad approaches:
- in conjunction with a companion desktop version of the same application (eg. OmniFocus, Things, Four Track)
- using a web service (eg. Darkslide for Flickr)
The web services are typically accessed via an AJAX API (or equivalent), but will obviously take longer for backups of large files. The desktop sync products provide their own (eg. OmniFocus uses a WebDAV server) and use an internal sync engine to keep things up to date, and can sync using the WiFi connection.
So either way, you are most likely going to have to write your own server to handle your own backups, and deal appropriately with the file types and metadata. I don't know of a third-party solution to this, but if one exists, it would be very generic, and may not suit your particular needs (eg. for file formats, etc).
So what is the standard way of taking backup of third party application data?
Write your own sync server and connect via WiFi. Start by looking at WebDAV, as you can build something on top fairly easily.
Is there any way by which we can save the data on MAC as well as Windows using iTunes?
iTunes will only do a full system backup. Your best bet is to write your sync server to be portable.
Is there any limit on amount of storage a third party application can take?
AFAIK there is no per-application storage limit on the iPhone. If you provide your own solution, you could do something like archive anything older than 30 days onto the Mac/PC, so you are only keeping recent files. Then allow them to choose "favourites" and those will be kept on the iPhone regardless of age.