unlike anti virus software which you shouldn't really have more than one installed you can install more than one anti spyware package.
Adaware doesn't run in the background, you actually have to run it manually and start the scan yourself so it will co exist with defender OK
and I would install zone alarm rather than rely on the windows firewall, the windows one isn't very good.. It's only one way for a start, it will stop incoming connections but does nothing about outgoing connections at all!