what does SERIAL and proc permissions stand for? Often in my rooted android device, since I have installed xprivacy manager, applications ask me for serial perm in category identification (hardware) (that very often, translation may be approximate), and sometimes /proc perm in same category as seen in the following screenshots. 
what are these perms? Should I allow or deny them?

 
Screenshots (click images for larger variants)
/proc/ is a filesystem that contains special files describing the current state of processes and the kernel.  

/proc/mounts contains information on the current mountpoints. Mountpoints are similar drive letters in Windows.  Since there is only one file hierarchy in Linux, any file systems that aren't the operating system's FS (like an SD card, /proc , etc) need to be grafted onto this solitary tree.

Details on these graftpoints are accessible by reading /proc/mounts.  Part of the info that can be retrieved from this file is the current space utilization and capacity of each filesystem.

Because it's a file system usage utility, this app probably needs this info in order to tell you how much free space there is on the SD card and/or the main OS filesystem.

Serial permission allows the app to grab a unique identifier for for your phone.  I'm not sure specifically how this app intends to use it.