As far as the icons go, the following tutorial covers the procedure to restore both the icons you mentioned: Desktop Icons
Do your drives show up in Windows Explorer?
Please attach a screenshot of Disk Management so we can see what it looks like as things currently exist. It will be easier than asking a dozen questions about what is or isn't there. We can then proceed from there.
Also, please update and run a full AV scan with your security software. Also, download, install, update, and run a full scan with Malwarebytes: http://www.malwarebytes.org/
. This type of problem can be caused by malware - so let's rule that out.
I hope this helps.
Thanks and good luck!