2. As for your second question: Small note next to a big note are called trills. It's a common musical ornament. There are all kind of musical ornaments. The one you were talking about asks you to play the two small notes briefly before the main big note without losing the rhythm.
3. As for you third question, I don't know this song yet. but I'll listen to it and if it's good I'll might post a piano tutorial on it in the future so stay tuned. :)
Hope I helped you with it. Don't hesitate to ask me any further question!