A zombie is a process that has ended but has not been cleaned up and removed form the process table. It is possible that it is waiting for a child, sibling or parent to end as well. Still sometimes zombies fail to ever get celaned up.
NI is the processes 'nice' value. A processes nice value dictates how it competes for CPU time. Processes can have a nice value from -19 to 19. Only root can assign a nice value below 0.
If you want a process to run without causing other processes to slow down you can start it with 'nice process'. This will give the process a high nice value, thus giving it CPU time that processes with a lower nice value don't need.
On the other hand, if you don't want your mp3 music to skip on a loaded system you may issue the command as root: 'nice -m -19 mpg123'
Take a look at man nice.