I don't know the exact limit but a tiny sample is allowed as part of another presentation. The YouTuber Techmoan has mentioned and respects these limits and plays audio during his equipment tests.

Playing full songs without a license can get your content (or even your domain or hosting) yanked over a DMCA violation report. Large infractions can result in lawsuits from media rights holders.

In the US, there is no exception to copyright based on the length of the clip used. In practice, though, copyright holders often ignore infringing uses if they are short and not commercial in nature -- but they don't have to, and they can change their minds at any point in the future.

If you're talking about using clips in an advertisement, though, copyright holders are much less likely to look the other way.

> Is there any way that smaller websites can play short snippets (10-20 seconds) of copyrighted famous songs on their website?

Yes. The legal way to do this is to buy a license. Usually, BMI or ASCAP are the entities that deal with this. You should contact them for terms. You might also want to consult a copyright attorney for authoritative advice rather than listen to an internet random like myself.

Fair use never applies to commercial.

In Canada you can pay SOCAN to get a general license for copyrighted content. It's not all content, but they have pretty good coverage.

Much easier to just find public domain stuff for an ad.