On the first example -- what is the significance of the character which is a circle within a circle? I'm assuming it's some sort of graphic or punctuation, rather than a kanji...?

The heading of that corner is just the pronounication of "m-take design" written out in katakana. The first line under the heading talks about the type of products the person works on (direct mail, leaflets, pamphlets). The second line talks about their specialities, as in the industries they focus on (cosmetics, health food), and then the last mentions they'll also do logo design, homepage design etc. I guess they wanted to emphasize the second line.

You'll sometimes see kanji-sized single circles used in Japan to indicate omitted characters (and you might see them on business card _templates_ as a sort of lorem ipsum, but unlikely on actual business cards), but this double circle doesn't have any specific meaning as far as I know.