“SecurID” will damage your computer

It's extremely unlikely to be malware as the Hazel program is a reputable utility that automates file actions by extending spotlight and file change detection systems of OS X. It does exist as a System Preference panel, so you could easily miss it's footprint on disk if it were not for the menu bar icon.

You can get updated versions and uninstall info from the vendor:

• http://www.noodlesoft.com/hazel.php

If you have Time Machine, you can use spotlight to determine pretty much precisely when it appeared.

Now, with the NSA and hackers and all sorts of people making software modifications and using back doors, your installation of hazel could be malware masquerading as an honest program. Without forensic analysis - it's hard to know. I'd start with reinstalling the latest version and doing a sanity check to make sure you're happy with it. If not, removing it should be easy and secure enough for most people.

Short answer yes but probably -- no.

You should definitely keep your videos. Don't delete them because you're concerned they could contain malicious data that could trigger errors in the video codec implementations that will lead to code execution on your computer. In fact waiting for some time will lower the likelihood of getting infected since any attack vectors will be invalidated in newer versions of codecs/applications. Keep your video players up to date. Don't use unsupported software which is not receiving updates.

If you like to still download and watch those cute movies and have a better conscience I would propose you install VirtualBox and a simple linux distribution for watching and downloading and have backups from your movies. Should that virtual system be infected by whatsoever thingie, just delete that virtual system and install a new one. Infecting a virtual system AND breaching the Hypervisor (the technique that drives virtual box, vmware et al.) is not very likely.

And remember to have BACKUPS! Then you are quite on the safe side. Let there be cat videos.

Adding to this, it may be also possible to share your media on your local network and watch it with guarded devices / OSs like an iPad running a non jailbroken recent system.

Some notes about downloads:

Downloading a file will not infect your system unless it is run or interpreted (like displaying a JPEG oder a Video or running javascript code). So browsing a site may infect your system, since the web-browser will interpret all kind of files not just the desired video. You could use a web scraper like jDownloader or something else to just download stuff from a given URL. My opinion is they do less interpretation. But who knows.