Is it necessary to get permission (due to copyright laws) just to use the name/title of a piece of music or song on cards in a game?
Use of song or music titles
Not really, but just because it is legal doesn't mean you can't get sued for it. Your safest bet is to parody the titles or stick with old standards from the Great American Songbook.
For example, a few authors, myself included, lift song titles as the headers for short RPG scenarios published in a gaming trade magazine. That said, the guidelines for some other publications explicitly state not to do this due to legal concerns. The chance of anyone getting sued is miniscule, the plaintiff doesn't have a leg to stand on, but it is an instance where it is typically cheaper to settle even if you are in the right than win a Pyrrhic victory in court.
What if you just wish to use, say ten seconds of a music track, minus any vocals?
That's sampling, which is very common, particularly in rap and hip hop. Look up the history of the "Amen Break," which is a 6 second drum snippet from "Amen Brother" by the Winstons that may be the most sampled loop of all time. Everyone on this forum has hear this sample, probably multiple times, whether they know it or not. Neither the performer nor the copyright holder have ever received royalties, and the latter considers its use plagarism. There is a fun site called http://www.whosampled.com/ if you are not familiar with how endemic sampling is to the industry. Some artists sample multiple tracks from different artists in a song.
Thirty years ago, when Grandmaster Flash and The Sugarhill Gang were doing it, you wouldn't have had to worry about legalities. That changed by the late '80s when sampling became more widespread and people started making money from it. Many cases have been settled out of court, which has perpetuated the myth that there are no legal ramifications. For example, M.C. Hammer settled out of court with Rick James and conceded a cut of the millions that he was making on "U Can't Touch This." It turned out that Rick James could touch it.
In general, record companies and artists turn a blind eye to sampling in the underground scene, and it only becomes an issue once the loop is on the radar and making money. One option is to buy pre-cleared sample discs, which contain tracks that you can use. Alternately, you can attempt to seek permission, called "sample clearance," but there is a good chance that the record company won't return your calls or will respond with a request for substantial fees. For a board game (something like Atmosfear, I assume) or a video game, you can probably get away with not obtaining sample clearance if you sell less than 1k copies.
You can argue fair use if you've substantially transformed the track and haven't caused significant harm to the copyright holder, which will hold up especially well with any tracks packaged with a board game. However, keep in mind that one judge ruled that _any_ musical sampling violates copyright. Outside of having clearance, any justifications you have are just building up a case for if the matter goes to court, with all of the time and cost that entails.
As of now, selling 1k copies of a game I make seems like such a far-off dream! I'm glad I'm relatively safe then if I use just a little tune here and there.. Thanks for clearing my query!
Just keep in mind that the same way of thinking became a problem for artists who were selling their records out of their car trunk one day and became a mainstream success the next. Also, I highly recommend incorporating as an LLC, if you haven't already, to protect your personal assets in the event of litigation, particularly if your work involves any plagiarism or infringement like this. Really, I'd recommend that for most people, as folding a company is much easier than filing for bankruptcy if worse comes to worse.
I guess I will just be more generic or do as you suggest from the Great American Songbook. Better safe thank sorry!