There are a variety of considerations related to your questions. MP4 is a short designation for MPEG-4. There are many different parts to MPEG-4 specifications. MPEG-4 Part 14 specifications are the media file format specifications most often followed by portable player manufacturers. MPEG-4 Part 14 specifications were based upon Apple's QuickTime data container format. MPEG-4 Part 14 containers can contain many types of audio and video files. However, some players that are advertised as 'MP4 players' are actually MP3 players that have the additional capability of playing AMV video, but that are not actually capable of playing MPEG-4 part 14 files or files with any other MPEG-4 format.
Apple has further confused that already somewhat confusing situation in its iPod players by starting to use the .m4a file name extension for unencrypted audio files and the .m4p file name extension for audio files encrypted by the 'FairPlay Digital Rights Management' system that it uses to encrypt music files sold through its iTunes Store. Most mobile phones (cell phones) that are advertised as being able to play MP4 files actually use 3GP which is a simplified version of MPEG-4 Part 12 which also is known as the MPEG-4/JPEG2000 ISO Base Media file format.
The 'bottom line' to all this is that it will be necessary to know the make and model of the player your daughter has to know exactly what types of files it is capable of playing.
1)Are they legal?
It may or may not be legal to download and use media files. Some copyright owners allow free use, but most don't. Reputable on-line music stores like iTunes pay royalty fees to copyright owners. Music files obtained from stores like that are legal to download and use. However, files obtained from unknown sources may be 'bootleg' copies that are not legal to use.
2) If I pay with my card will I be safe
Of course, there is some amount of risk when using a credit card to buy anything from anyone via the Internet, but that also is true when a credit card is used by buy anything by any other means. For example, any restaurant employee who has access to credit card numbers may use or sell them. The most important risk factor on or off the Internet tends to be the party payments are made to. I don't worry about using credit cards for Internet purchases from reputable companies, but I would be very reluctant to purchase MP3 files from unknown sources.
3) What will I get for me money? I mean I do not want to pay an amount to find that I only have the right to download one particular singer.
On-line music sales stores sell music a variety of ways, but most commonly they charge a small fee for each downloaded tune. Some stores allow some number of tunes to be downloaded after payment of a larger fee. Downloads are not usually restricted to a particular performer, although in some cases they might be. The bigger issue for most on-line music customers is the right to play downloaded music on more than one player. Customers generally would like to be able listen to tunes they pay for on a portable audio player, on their computer, in their car, etc., but most on-line music stores encrypt music files in ways that cause them to be usable only on a single player.
Another important issue related to your daughter's player is file encryption compatibility. For example, tunes purchased from iTunes can be played on Apple players like the iPod or iPhone, but not on most other players. It will be necessary know which player she has to give more specific advice.
-Bob