There is no need to shut down ZA to install avast. The problem with ZA conflict was related to the Pro versions privacy function, which isn’t in the ZA free version.

NAV can be a bit of a pig to get rid of and you may need other measures, use the add remove programs to uninstall it. If you experience any remnant issues then you may need to go further.

A link worth looking at, which is a program removal tool that can remove the remnants of a number of different Norton Programs:
Removing your Norton program using SymNRT
You can also download SymNRT, a Norton uninstall tool that uninstalls all Norton 2004/2005/2006 products.