Good Day CAM,
Sorry I am a bit behind on the original posting here. Hope you are still around checking in on occasion.
As mentioned, the square groove is only for that. D1.3 is no where near as wide ranging as D1.1. While there are a handful of PreApproved joints (which do happen to cover the vast majority of applications to D1.3) the welder qualifications to them do not overlap nearly as much as in D1.1. Grooves do not qualify for fillets. Without my book in front of me, the normal coverage for welders is to test them on fillets of a thickness that covers the range you need and then flare bevel or flare V grooves.
I generally test them, based upon mostly testing welders for construction applications, in the vertical position progression downward. This qualifies them on the flare bevels and V's for studs and other shapes in F, H, and V down. Then I test fillet welds also in the vertical down progression position. There are times when an overhead is also added to make sure someone on the team is all position qualified for those times when it just can't be done any other way.
Now, having said that, D1.3 is a code you really need to get into and/or hire a consultant to help you through the first time around. As in D1.1 and D1.2, there are things that must be watched carefully pertaining to differences between Welder Qualification, WPS development, PQR's, etc. Most PQR's, WPS testing, is easy in D1.3. Just takes a wedge, hammer and a good vice.
Any further questions, just ask away.
Have a Great Day, Brent