1) See my post, the second paragraph tells how to set iTunes preferences so that it automatically downloads your new app purchases when you star it.
2) It used to be essential to have your apps backed up in iTunes. Now it's just a convenience, a second way to restore apps if they go away. It can also be handy if you want to restore/sync your apps to a new device, or after restoring the old one. While you can do all this from iCloud, using iTunes with a USB cable is much faster.
As far as free goes, there is no more reason to put purchased apps in iTunes than the free ones. All apps, once purchases, can be downloaded again for free from the Purchased tab in the App Store.
I like the extra backup of my apps in iTunes. It is rarely useful, but there are occasions when it might be. For instance, if you update an app on the iPad but decide you don't like it, or it's broke, having the older version in iTunes is the only way you can go backwards. Of course, that only works if you haven't synced or manually updated iTunes since the app's update.