There is not much point in using D for program installation because you would have to re-install the programs anyway in the event of a major C drive crash.
It is a good idea to have data and saved/downloaded files go to anther drive, and you should do this. Office productivity suites give you the option to send/save to a path other then the default C drive folders.
Re backing up. Were you to save all of your important stuff to D, it would make the backup process more simple because all of your important stuff would be in one place, isolated from all of the other files needed to make the computer work..
BUT, you should not see the D drive as backup because it isn't. You have not backed up your files until they are safely on a drive which can be isolated from the computer, for example an EXTERNAL hard drive..
The idea behind using an external drive is that, in the event that the main, and maybe only, hard drive in the computer fails, or you have to re-install your entire computer, your data is still safe on the external drive, and can be re-instated easily..