You don't. "It's his dog" would also be "E' il suo cane". It's like in English where you can't tell the gender of the owners from "it's their dog". In Italian, suo vs. sua tells you the gender of the object being owned, not that of the owner.
No, the article "il" is necessary here. In general, his/her = il suo/la sua/i suoi/le sue. In some cases the article is dropped (for example in front of family members: "sua sorella", and not "la sua sorella", suo padre, sua madre, etc.).
I think I've sussed it. In English we give the pronoun gender, in Italian you give the noun gender. I and you does not have gender, so why should he, she and it not just be simplified to "it". Makes sense. Yes? No?