Ultimately you want to be able to transcribe using your ears and not eyes, so you will want to train your listening skills (visual guidance is always good for confirmation, but try to not depend on it!). For beginners or if the piece is too complicated for your skills, it is always helpful to find covers of the song in youtube with the specific instrument isolated (if the song is popular this will be easy to find)
Training your listening skills takes time but will be most important in your musical development, so transcribing things like this should become a regular practice for you. Start by getting used to finding a note in your instrument and being confident in your ability to do so. Transcribing a line means you should be able to hear the line, sing the line, and find the notes in your instrument.
Something that will facilitate this a lot is interval training. Learn to hear and recognize all intervals. This doesn't take as long as you might think at the beginning and will drastically improve your listening and transcribing.
Finally, don't worry too much about "not sounding as good as the original". Usually what you listen to is a product of professional musicians and a professional studio recording with a lot of production involved, with carefully chosen sounds and mix. Just aim for replicating the main idea, in a way that you feel comfortable playing.
To answer your points: It sounds like he is doubling the melody with both hands, adding sometimes supporting notes. This is not super easy to hear, as the guitar is also playing unisono, and both instruments are playing in a similar range.