1 - Yes, a Fox HS as I do on my street bike.
2 - Yes. Regular style bash hat.
Ref answer no. 1, the Fox HS is more like a BMX bash hat and has a much thicker outer shell and far fewer vents, hence the HS. I thus think it better for city work as things you're likely to nut on the street will probably be a lot harder; cars, pavements, kerbstones etc., than in a rural environment.