Do I have to listen to the song repeatedly if I want to sing it well? What if it doesn't sound as good as the original?

Although you will have to gain a good deal of familiarity with the song in order to sing and play it, it's not so much a matter of listening to the song repeatedly as listening to it critically to understand and appreciate its construction and nuances that make it unique. As the original is likely performed by a professional with years of practice and experience, you can expect that unless your skills match the performer's, it won't sound as good. However, with practice it will sound better, and the great part about covers is giving it your own individual twist.