I'm not sure what Conduit Search is, but if you didn't put it there then you should probably get rid of it. You should take a look at the Knowledge Base article How to set the home page. Your homepage might have been changed by a particular site. Sites like MSN, Yahoo, etc have been know to ask to become your homepage.
There are steps in that article to reset your homepage preferences to default. I would try that first to clear out any strangeness. If that works, you can try setting your homepage again to your personal preference.
For search, you should take a look at the Knowledge Base article Use the Search bar in Firefox. Your default search might have been changed by a particular site. Sites like MSN, Yahoo, etc have been know to ask to become your homepage and change your search engine.
Appreciate your rapid response! You have given me what appears to be a
great selection of ways to go. The fact that you(and everyone else I have conferred
with) are not familiar with "Conduit Search" heightens my concern. I will definitely
keep you posted.
Conduit Search is a form of spyware / malware. It is best to uninstall it, then run Malwarebytes anti malware to fully ensure it's removal.
Download and Install MalwareBytes Anti-Malware, run a full Scan. http://www.malwarebytes.org/