Ok, there are a couple of things going on here ... I just visited the website:
http://solutions.liveperson.com/
Then I looked in Safari Prefs ~> Security ~> Show Cookies and did a search there using the search field in the upper right of the window, for LivePersonID. I saw there were 8 cookies there called LivePersonID. Basically you can just delete them if you want ... they usually remember some basic log-in details that you may or may not have allowed if you were surfing at the website.
I would strongly advise you also go into Safari Prefs ~> General
Make sure the "Open 'safe' files after downloading" box doesn't have a tick in it. This will safeguard your Mac in the event that something is downloading without your consent. It's good that you were quick enough to terminate the download ...
As Greenman pointed out, never allow a website to scan your mac for viruses ... those links can never be trusted.
As far as I know ... there are no viruses for Mac OS X but there are some nasties that can take over your web browser but they usually only find their way onto your mac through you clicking on a box that pops up telling you that some app is out of date and you should click here to download the latest version. Usually it's Flip4Mac that's used as a con to get you to download stuff that interferes with your web browsing capabilities. I've only known this to happen to people who surf porn sites.
With regards to your OnyX querie ... it's asking you to start up your Mac using the original install disc that came with your Mac ... pop the disc in and restart your Mac and hold down the C key just on hearing the startup chime.
Then just go through the Language Selection and then you will see some menu items ... I think it's either Tools or Utilities ... just pull down the menu and you'll see Disc Utility. Once it launches select the First Aid tab, then your Macs HD in the left column and click on Repair Disc.
Then restart your Mac. OnyX is a good tool to use to keep your Mac in tip top shape. You need to run it from an Admin acct and I should point out now that you should have 2 accounts on your mac ... one that is a Standard acct for every day use and the other is an Admin acct for important installations etc and for running OnyX. This is good housekeeping practise.