(Barbarian shows lighthouse a skeleton of the earliest known whale)
So, what features does it have that are only found in whales?
The skull, mostly. The teeth and jaws are those of whales, and the sigmoid bone in the ear is only found in whales, and this one has it, and the nostrils are set back on the skull somewhat.
The first hint that they were probably right came in 1983, when researcher Phil Gingerich found a 52-million year old skull in shallow deposits in Pakistan. Although fragmentary, the skull had teeth that were nearly identical with those of Mesonychids and the Archaeocetes. The configuration of the bones at the rear of the skull, however, were different from those in the Mesonychids, and were identical to that of the Archaeocetes. Gingerich thus concluded that the animal, which he named Pakicetus, was a very primitive whale. "In time and in its morphology," Gingerich reported, "Pakicetus is perfectly intermediate, a missing link between earlier land mammals and later, full-fledged whales." (Gingerich, The Whales of Tethys, Natural History, April 1994, p. 86)
http://www.fsteiger.com/whales.html
Ironically, the first specimen was only of a skull, and people were very surprised to see that the next one was connected to the skeleton of an ungulate.
And, yes, I would like to see some more "evolved" versions.
Sure. Here's a somewhat more evolved whale...
http://members.cox.net/ardipithecus/evol/lies/images/ambulocetus2.jpg
Ambulocetus had an even more whale-like skull, more adapted for hearing underwater. But it had functional legs, and could still move clumsily on land, a bit more so than a sea lion. And the oxygen isotopes in the teeth indicate that while it was capable of venturing out to sea, it still had to return to land to drink fresh water.
And then there's...
http://www.palaeos.com/Vertebrates/Units/520Cetartiodactyla/Images/ProtocetidaeA5.jpg
Rhodocetus was larger, and with smaller legs that would have made moving about on land rather difficult (but still possible) and the oxygen isotope ratios in the teeth now show that it drank salt water, and therefore did not need to return to land at all.
And then...
http://www.toyohaku.gr.jp/sizensi/03event/tmnh-h16/tmnh-h16tokuten/dorudon1.jpg
Dorudon was pretty much like Rhodocetus, but much larger, with smaller legs, and the pelvis was no longer connected firmly to the spine. It could not leave the water at all.
And then...
http://daley.med.harvard.edu/assets/Willy/Basilosaurus.jpg
Basilosarus was truly huge, with even smaller legs, and the rear legs were now tiny relative to the huge body.
There were other trends as well. The nostrils of these are gradually moved farther back on the skull until in Basilosaurus, they are almost like the modern blowhole.
And the spine changed gradually from a very rigid ungulate spine to an extremely flexible whale spine. And this transition explains why whales have horizontal flukes. Ambulocetus had large, wide feet, like that of an otter, and swam by vertical undulations, as an otter does. And more evolved whales with broader tails, used the same motion, which required a horizontal fluke, rather than a vertical fin.
I'd like to see the "process" that took that and turned it into a whale.
This is only an outline. You might want to read "At the Water's Edge" by Carl Zimmer, to get more detail. It's a fascinating and well-documented story.
Also, if there were no platypuses would you think Ducks and Beavers evolved from them, since they have features that are only found in ducks,
Platypuses have no features found only in ducks. They do have some features found only in reptiles and other monotremes, however. The "bill" is just a figure of speech; it is not remotely like the beak of a duck, although it does resemble the "bill" of some extinct reptiles. Since genetic studies show that they are not the ancestors of placental mammals, I would not think that they are ancestral to beavers, either. Beavers are more closely related to the advanced therapsid reptiles,(they share a simplified mammalian shoulder girdle) and platypuses don't have any features found otherwise only in beavers.