Basically drag and drop for music and pictures. Create folders on your SD Card and simply copy your pictures on it.
As far as apps are concerned it can be done by setting>manage app it will show move to sd card.
With reference to your Question i am providing you the link with similar case. Read it may be it help
http://www.tomshardware.com/answers/id-2043293/external-hard-drives-recognized-laptop.html
If your HD hasn't been detected anywhere then it is dead i suppose. Try for new HD as this wont last anymore now. Try to take out important data through software or services which ever is suitable to you.
Recovery of data has been easy now. You donot need to worry that much. I can say that becoz i experienced it. You can easily leave that to data recovery technical person. Stellar Data Recovery http://www.stellarinfo.co.in/services/hard-disk-recovery.php
And also go for new drive dead drive wont...
Do not mess yourself so much if you have not idea regarding the recovery. Initially as people already explained you not to format the drive otherwise recovery would not be possible. Secondly Yes go for the recovery software they help you finding your files.You can check Company like Stellar Data...
In this case data recovery option would be beneficial. My advice would be not to overwrite anything on the disk because recovery would be tough then. Also do not format it again.
Checkout this link i hope you will get your solution...
Yeah broken HDD data do get recovered. Did you take any software help? Try Recovery software first and if it does not work then second possibility would be Recovery Services. As far as i know they provide consultation before the starting of recovery. In your case nothing can be done except this...