Is it possible to learn how to sing on your own? How would you describe these singing styles?

You could only have your own style if you are already singing your own songs. Try singing every song you think is hard. It will improve you. Don't just sin the new ones. Standard songs are also great. If you want to be a singer make sure you know the standard songs. Older people will appreciate you more if you sing this. Young ones will only appreciate the new songs.