1. There are some songs that are easier to sing and play at the same time than others. Some I can do easily, some are far trickier. For me the most difficult some to sing and play at the same time is AC/DC TNT. Each part taken alone is fairly easy. Put the two together and you really got your hands full. It has to do with the timing relationship between the two. Try it some time.
2. People (Stars) usually sing their own stuff. They wrote it and perform it in a way that is natrual to them. Most don't play and sing during more difficult parts.
Like any thing else practice makes perfect. Break the song down and focus on parts that are givving you trouble. Listen for how the two parts go together, and look for ques to keep you on the right track.