You’re 3 for 3 with answering your own question. Yes, italicize the words being sung. Yes, surround the singing bits with quotation marks as you would any dialogue. And yes, if a couple of lines or more (perhaps entire verses) are being sung, then set off the passage from the rest of the narrative text with wider left and right margins (this is called an “extract”). Two of your paragraph tabs will make a nice margin depth. You can see this treatment in Curse of the Blue Tattoo, from L. A. Meyer’s spirited Bloody Jack Adventures series. That said, if your character is just singing a few words or a single line, ditch the special margins and just incorporate the italicized lyrics into the narrative as you would any short bit of dialogue, complete with beginning and ending quotation marks.