Is it possible to create or use an existing web-player to play grooveshark songs? Actually there are only two widgets, one for single songs and other for playlists. Would it be possible to use any other player?
No. They provide their own api for embedding into other applications/web pages. Only their api will understand what the backend file fetch location resolves to and they have a security to allow only their api to access the file location.
It is possible to write/use your own jukebox only if you were able to crack the permalink of the song that is obtained from the server... which is practically not feasible.
Grooveshark provides a nice widget. You can use it. If you want more customizations, do it on your webapp and modify the surroundings..