Yes and probably. If the Sidney is in script print it's a product of the Sidney Hollow Ware Co. and probably predates Wagner. However, Wagner ended up buying the Sidney Hollow Ware Co. to increase production of its wares. I believe the old Sidney Hollow Ware foundry was where the "SIDNEY" pieces were made and those pieces were just like Wagner's regular marked pieces. In fact, you can often see where WAGNER was removed from or filled in on the pattern. WAGS reprinted a nice SIDNEY catalog c.1905 and all those pieces are illustrated. Obviously they are Wagner items from the style, etc.
National was a cheaper line of skillets plus a waffle iron made by Wagner (I don't think they came from the SIDNEY foundry however-whoops, just checked my catalog and there are NATIONAL skillets listed). Being that SIDNEY and WAGNER ware were made by the same company anything would have been possible and the National skillets might have been made in the main Wagner plant yet included in the Sidney catalog...or they may have been made in the SIDNEY foundry, too.
The National skillets in sizes 7-9 only were slightly smaller in diameter and a bit lower than regular skillets and were made to offer a cheaper, price-competitive skillets to meet the competition. National waffle irons had less features than the regular Wagner line.
I don't know when the SIDNEY ware foundry was shut down or sold or what happened but it did go away eventually. National skillets were made for many years in a few variations. Covers were made for the Natiional skillets but are very hard to find.
Steve