Avast ver. Internet security 2015,
So I understand that web shield is meant to be a malware blocker but I was recommended
a malware detector and remover called Hitman Pro (second opinion malware detector)
by cyscon phishing firefox add-on.
It detected 10 threats and 135 trace files in the form of cookies and adware.
Is web shield not meant to prevent this?
Since running this software there has been a noticeable speed increase (Faster) at start up
It detected 10 threats and 135 trace files in the form of cookies and adware.avast does not target cookies as they are not malicious
the rest, impossible to say without you giving more detailed info
anyway, NO security program have 100% detection or zero false positives
a malware detector and remover called [b]Hitman Pro[/b]Have not tried that for a very long time. As i remember, the free version only removed what it detected for a limited time?
a better tool is Malwarebytes free, it will remove what it detect all the time 
Hitman Pro has form for not only finding malware but removing legitimate files, some of which can have an adverse impact.
The general advice is not to run it without guidance - this advice from one of our very experienced malware removal specialists.
Your system your choice.