I've owned many Macs over the past 10 years. We currently have multiple iMacs, MacBooks and a Mac Pro and I have never run antivirus protection on any of them and have never had a problem with a single virus.
I've never bought anti-virus for Mac and I've been using Macs since the early 90s. If you are looking for a good housekeeping app, I highly recommend CleanMyMac 2 from MacPaw. I use it regularly and it does a fantastic job keeping things tidy. I never have any concerns that it's going to go rogue and delete important personal or OS files.
It's pretty unlikely that that would cause a problem, but it depends on the way you're downloading it. If you give it your password after downloading music, it could have actually been malware program that you downladed. MP3s never require installation, so you're not providing your master password. If you install pirated software, you give it your password and it could have bundled malware that installs along with it.