1) Specific to any particular ethnic group and/or region?

Very common in German bank barns of Pennsylvania.

2) Were these absolutely structurally necessary, or just an insurance measure employed by the carpenter to stiffen or triangulate the bents/bays and to be used in conjunction with the "standard" braces (post to tie and/or plate)?

In context of forebay bank barns, the down braces tend to be very long as such there really is not a substitute to length. In exterior wall braces can run sill to plate or sill to post. In some cases I believe the long sill to post braces are part of the raising scheme, once the brace is set to post a strong structural element is in play, that maybe used as an anchor for pulling up other framework. In bents the long braces sometimes were employed as truss struts to support very large cantilevers in the forebays. The wall of forebay was in some cases a parallel chord truss with very long struts. So the long down braces can serve in various manners, besides windbracing.

3) Do these "down braces" generally function in compression as standard knee braces do?

Lacking specific tension joinery, yes in compression, however with the right connections why not engineer for tension, if needed.

4) Do any of you traditional framers employ these in your work?

I have.

You will also see downbraces on corner posts in early light frames with heavy posts and balloon frame infill.