(G and F clef) Talking about G clef: What I understand is, you play D and B (same duration, 1/8) and then C. But on the interpretation of the score on this youtube video, it seems that there are two voices, since D has the duration of a quarter note, and B and C of an eighth note. Shouldnt D be written with the stem pointing down? (since it has a different duration as shown on the video). If the sheet music corresponds with the playing on the video I linked, how can I know D has a duration of a quarter note on the sheet music I attached).
You can't. This might just be a lazy arrangement that didn't bother to represent the voices clearly. (This is quite common in pop transcriptions that may not try to give all the details.)
You're right that if you wanted to more accurately represent what the piano player is doing in your linked video, there should be a separate quarter for the D with a downstem.