First-time dancers will likely find experienced dancers extremely friendly and helpful. If this does not seem to be the case, talk to the dance organizers. Or, depending on your location, you could find another dance group. At most dance events in North America, we dance with a different partner for each dance, although dates who attend together and significant others might dance with each other more than once. This is 1999.
Women can ask men to dance.
At a contra dance this is certainly true and has been for some time. It might be just as common as men asking women, or more so. Contra dancers make eye contact whenever possible. This adds to the connectedness of the dance, and helps reduce dizziness, especially during the swing. It is also uncomfortable for some.