Of course you can move all data from C to D. Generally speaking you should save all data on partition D. If something goes wrong with OS and you will be forced to install OS again you can format partition C only and all your important data on D will be still there.
If you think on Windows libraries you can leave them on C but you can create own folders structure on partitions D. If some application must pick up certain info than you must be sure that certain application can find it. Due to this check available options.
You can copy the contents of your whole user folder (if it is not too big!) from C: to D: e.g. c:\users\fred\
Then if you right click on each of the libraries on C: (documents, music, videos etc) and select properties you can include the new folder location on D: and after remove the folder location for C:. Then when you click on the library it will take you to the files on D: instead of C:.
For 'downloads' you will need to change the browser options (e.g. in Internet Explorer, Chrome etc) to point to the new 'downloads' folder on D: so that it saves them there.
Same thing with iTunes and other applications you use.
You can change the location of almost everything including important things like 'desktop', 'favourites' and 'contacts'.
If you restore your C: drive you won't lose anything. You will just have to add the locations to the libraries to point to the files in D: again. 5 mins work instead of hours restoring backups of your files!