See the details in this informative paper below, with actual fossil evidence.
Ask me anything about the science of Evolution :)
There are lots of fossils now showing all the stages of progressive adaptation of the whale line from land to water.
Yes all of them are mammals, obviously.
Yes there is a gradual increase in size.
Here is brief description from scientific sites
4)The earliest known archaeocetes were creatures like the 53-million-year-old
Pakicetus and the slightly older
Himalayacetus. They looked as if they would have been more at home on land than in the water, and they probably got around lakes and rivers by doing the doggie paddle. A million years later lived
Ambulocetus, an early whale with a crocodile-like skull and large webbed feet. The long-snouted and otter-like remingtonocetids appeared next, including small forms like the 46-million-year-old
Kutchicetus. These early whales lived throughout near-shore environments, from saltwater marshes to the shallow sea.
Pakicetus and Icthyolestes. Earliest archaeocetae (archaic whale ancestors)
3)
Ambulocetus.
Unlike pakicetids, ambulocetids show obvious bodily adaptations to an aquatic lifestyle, such as reduced limbs and very large feet suitable for paddling. Their hindlimbs, also strong enough to support their weight on land, and possibly acting together with a dorsoventral undulation of the spine, probably were their main organ of propulsion in the water. A tail fluke had not yet evolved. Because hind-foot paddling is not a particularly effective way of swimming, it is unlikely that the carnivorous ambulocetids actually chased their prey. Rather, they probably ambushed it from the water, in a way strangely similar to crocodiles.
2)Protocetids (Proto whales) the oldest group to include the first fully marine cetaceans, lived about 39-47 million years ago. They were also the first cetaceans that finally left India and, indeed, the ancient Tethys Sea, and specimens of various protocetid genera have been found in both Africa and North America. As may be expected, protocetids from the Indian subcontinent include the oldest members of the family and comprise the genera
Indocetus, Rodhocetus, Babiacetus, Takracetus, Makaracetus and Artiocetus. Protocetus, Eocetus and Pappocetus occur in Africa, whereas Georgiacetus, Eocetusand Nachitochia are found in North America.
Rhodocetus
Maiacetus (mother whale) is a fossil of this type. The fossil is found with a fetus inside her. It was an aquatic whale ancestor, that came up to land to give birth.
Maiacetus fossil (male)
Female with baby.
1)
Dorudontidae were the first lineage to fully leave the land and give birth in Ocean as well.
Dorudontids are closely related to both basilosaurids and the two families of extant cetaceans, mysticeti and odontoceti, and indeed probably gave rise to both. They were considerably smaller than basilosaurids and, rather than having a greatly elongated body shape,
had proportions resembling that of modern cetaceans. Similar to basilosaurids, their pelvis no longer attached to the vertebral column and their hind limbs tiny,
and could thus no longer support their body weight on land. A distinct ball-shaped vertebra in their tail indicates that they possessed a tail fluke and their mode of locomotion is likely to have been similar to that of modern whales. They are found in 35-38 million year old fully marine deposits all over the world, indicating both a wide distribution and complete
independece from freshwater.
Thus one sees the gradual transition of a land living mammal lineage to fully aquatic whales in a space of about 20 years (53-33 million years ago)