It's not legal to use a song on a website without permission, not even a single second of it. There's no fair use for even a snippet. Facebook will mute the audio on a live video stream if the audio features, for example, music playing on a radio station in the background, because the user doesn't have the right to disseminate that.
Morally, it would be improper as well. What if the artist disagreed with the content of said website? It would be akin to a political campaign using a song (which they're often asked or told not to, Bruce Springsteen telling Ronald Reagan to knock it off being a prime example).
One can acquire a blanket license from ASCAP or BMI to use music on a website, but that would cost anywhere from $250 to $2,000 annually. Even the lower figure of the two would be a poor use of a company's digital marketing budget.
As for embedding YouTube videos, a clause in YouTube's Terms of Service states "You may also show YouTube videos through the embeddable YouTube player", and this is affirmed by a 2007 legal precedent which I found that indemnifies a website publisher from infringement liability for hosting embedded YouTube videos.
However, it's good etiquette, as with the campaign songs example above, to ask the video publisher for permission, or, if it's implied by the video being shareable in the first place, to offer a notification that you intend to embed the video. Just as with the ADA, good web design doesn't need government force to prevent bad business.
If your site is directly involved in transactions, make sure you acquire a SSL (Secure Sockets Layer) certificate, which encrypts the link between a web server and a web browser. This will ensure that your customers' information will not be compromised.
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