Thinking about Sewers as "above the line" or "below the line" isn't a productive approach. Sewers doesn't change the abilities of other cards the way, e.g., Inheritance does. Just think of it as like Market Square—a special effect that is activated when you trash a card.
Since Rats' and Sewers' special effects are both activated "when you trash" something, they happen at the same time and you can pick the order. So yes, you may trash two Rats, draw two cards from Rats' special effect, and then trash two more cards with Sewers. Or you can do it in the other order if you prefer.
I'm not quite sure about the answer to your second question. Usually when multiple cards are trashed, they're trashed simultaneously. This would mean that, if you trash two cards normally, and then Sewers gives you the right to trash two more cards, you have to select and trash both cards before activating the on-trash effects of either (meaning you can't trash 1 Rats with Sewers, draw a card, and then trash a second card with Sewers). But the text of Sewers doesn't say "trash up to n cards"; it says "trash a card" and it's an effect that can be activated multiple times. So maybe it's like Monastery, whose phrasing is similar, which does trash one card at a time, activating on-trash effects in between.