The two gaiwans look very iffy to my eyes. Granted, I am looking at photos on my monitor, so the colors might be off, but there are a number of issues that would still cause me to steer clear of them.
On the "1913" gaiwan, adding to what TomVerlain said, those wax seals mean virtually nothing. I can buy them with adhesive tape on the back, which the 1913 one seems to have showing underneath. If you want to spend the money to be more authentic, you can go to any seal carver and ask them to carve you the same seal, and then buy the wax. It is pretty common here. Just to make it clear, I have never, nor would I ever do such a thing!!! I would say the gold is way too perfect to be authentic. The thickness of the strokes on the flower and leaves, and characters look is fishy to me. The way the characters were painted, and the thickness of the strokes, sets off alarms. At the time, anyone who was literate was capable of writing small characters. It was the norm. The strokes go from thick to thin, to thick, and these are just thick. Now, writing tiny characters with a brush is a pretty rare art. Even most calligraphers are not very good at it, because there is little call for it, so the fact that the strokes are so uniform in thickness make me think they were newly created. There is no artistry to them and such writing should have been commonplace for a porcelain decorator in the Qing Dynasty and Republican Period. The red characters on the bottom and the lid are also a little off for the Republican Period.The wear to the gold line on the rim is also odd. The gold on these pieces rubs off so incredibly easily and yet this one's design is virtually flawless, the missing gold does not look like it was worn off, but flaked off. There should be some wear somewhere if it was ever used or even handled much.
On the "Qing Dynasty" gaiwan, the red seal on the bottom and on the lid, is the wrong color. It could be my monitor though, or the photograph. The wear on the gold is very fishy. It is scratched off in bits, but there is no place where it looks worn off. If this piece was truly over 100 years old, there would be some wear on it somewhere, unless it was hermetically sealed and never touched or used. The colors of the leaves and flowers are off, but again, that could be my monitor or the camera's doing. The design and style of the design is not quite right for the period also. If this was a real piece, it would have been a fairly expensive piece, yet, the lip looks like it has little chips, and they just painted the gold right over it. I do not believe they would have just covered over the chips, at least I have never seen it before and I have seen a fair number of antique gaiwans. Quality control was better than that. Also, the gold rings, especially on the lid, are really thick for such an apparently refined piece. The thicker gold rings generally were on the poorer produced pieces.
To sum up, there are just too many questionable aspects to them for me to believe they are antiques. Of course, if you think they are really fantastic and you do not mind if they are antiques or not, then go for it.
Another thing that sort of bothers me, is that all of the products on the website are very common, unexpensive pieces, but they have found two expensive antique gaiwans. Intact gaiwans with lids are pretty hard to find in such condition, and logically speaking, they just do not fit in with the rest of the items offered on the website.
Anyhow, that is my two cents worth.