The three antiyuckware apps shoildn't conclict with one anther, though its possible that during scans, they'll pick up stuff in their compatriots' databases or quarantine files - a nuisance, not a problem.
On the other hand, running the real-time active protection components of all three simultaneously will be a hefty resource load, and unless you've got a very fast processor and tons of RAM, there's gonna be a noticeable performance hit. My suggestion would be to pick the one you find most satisfactory for real-time protectin and blocking, and configure th others to not start with Windows, keep them updated manually - say launch 'em and have them check for updates once a week, and use them just for scan-and-clean operations., on a schedule, and/or on demand, as you feel appropriate.
Your Norton/Symantec issue sounds as thoug Windows Security Center is unable to detect Norton's status. 2 things to try here - one, launch your Norton app and use its "Live Update" function; Automatic Updates does grab the antivirus database updates, but may - very well may, not retrieve application patches or updates. Make sure your Norton installation has all the most current updates and patches. When you've downloaded and installed all Norton updates, reboot, and Norton should present you a prompt which will ask if you want to allow NAV to report its status to Windows. The default setting is "No", so be sure to change it to "Yes". That oughtta do the trick - I think. If it doesn't, then I'd suggest you uninstall/reinstall NAV, run Live Update again, reboot, and watch for the prompt that asks if you want NAV to report staus to Windows.
More info from Symantec
HERE.
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