As we are running out of space, we would like to archive all the old documents and move them to different disk/tape.
If I search for a archived document, it should be able to fetch it back.
If you are using Alfresco Enterprise the you can use policy driven storage to move your content between disks.
Otherwise depending on your O.S. and disk tools you may be able to mount your different disk under your content store and move some content onto it. Or simply move your entire content store onto another disk.
Could you also tell me if there is an option of taking selective backup.
I understand the folder structure of the alfresco. All the documents uploaded in the 10th month will be saved in 10 folder under alf_data/contentsote/2012/10.
So after every month, is there a way to take monthly backup and restore them?
Yes indeed, that's one of the reasons why the content store is laid out the way it is, it lends itself to a simple incremental back up plan.