I recommend that you remove it for the following reasons:
Adware or advertising-supported software is any software package which automatically plays, displays, or downloads advertisements to a computer after the software is installed on it or while the application is being used. Some types of adware are also spyware and can be classified as privacy-invasive software.
You are fine on the antivirus program. It appears that the member didn't realize that Alwil Software makes Avast.
Other than the one adware, the system looks good.
EDIT: It wpuld be a good idea to run an online AV scan. The Avast log appears to be fukk of errors and I don't know that it is running correctly: Run Eset NOD32 Online AntiVirus Scanner HERE
Note: You will need to use Internet Explorer for this scan.
Tick the box next to YES, I accept the Terms of Use.
Click Start
When asked, allow the Active X control to install
Disable your current Antivirus software. You can usually do this with its Notification Tray icon near the clock.
Click Start
Make sure that the option "Remove found threats" is Unchecked, and the option "Scan unwanted applications" is checked
Click Scan
Wait for the scan to finish
Re-enable your Antivirus software.
A logfile is created and located at C:\Program Files\EsetOnlineScanner\log.txt. Please include this on your post.