1. Yes, e.g., ごぞんじのように or ごぞんじだとおもうんですが or ごぞんじですか.
2. I'm not sure what you mean, but する is the most common word for "to do", I'd say, with やる also being up there, although it has some other, more specialized meaning.
3. Not quite. で is the -te form of だ. だって has meanings of "but" and "also".