You are using a rather specialized pair of displays that are know as cladograms. This is likely the first time you ever heard that word. I'd suggest that you drop the topic here, admit that have no idea of what you are talking about, look at the following two sites:
http://en.wikipedia.org/wiki/Cladistics
http://users.rcn.com/jkimball.ma.ultran ... Cladistics
The fish on the diagram are currently extant fish.
I do not expect that you will take my advice, so here's a simplified explanation: Look at the first diagram carefully. Note where some significant advances are indicated: Jaws, Lungs, Claws or Nails, Feathers, Fur; Mammary Glands. To one side (the down side) that advance did not exist, to the other side (the up side) it did. Thus (in a simplified sense) the development of jaws is what distinguished the hagfish we are all descended from, from the bony fish that we are all, more recently, descended from; and the development of lungs similarly distinguishes the amphibian that we are all descended from from the bony fish that came before and that gave rise to both our line and that of the salamander. In the same fashion the development of feathers (which I'd argue covered more than just the birds) separates the feathered reptiles (some of which became birds) from the mammal like reptiles that evolved the fur and mammaries that are the mammal's calling cards.
stcordova wrote:
What? Real DNA of existing organisms don't suggest we descended from fish? Exactly my point. The only place where it is "proven" we evolved from fish is in the imagination of the evolutionists. It surely isn't indicated by existing (extant) data.
You're the one who doesn't understand the diagram. The mammals don't nest within the fish as is clear in the bone morphogenetic programs! Ergo, mammals didn't descend from fish, fish descended from fish.

Yes, real DNA of existing organism does show that we are descended from fish, we can trace DNA back as far as you want to go. Hagfish to Boney Fish to amphibians to reptiles to mammals. In fact there are numerous lines of data that lead to that conclusion, not just DNA, here are but four of them.
Wiki:
1. "Evolutionary developmental biology and embryonic development - Evolutionary developmental biology is the biological field that compares the developmental process of different organisms to determine ancestral relationships between species. A large variety of organism’s genomes contain a small fraction of genes that control the organisms development. Hox genes are an example of these types of nearly universal genes in organisms pointing to an origin of common ancestry. Embryological evidence comes from the development of organisms at the embryological level with the comparison of different organisms embryos similarity. Remains of ancestral traits often appear and disappear in different stages of the embryological development process. Examples include such as hair growth and loss (lanugo) during human development; development and degeneration of a yolk sac; terrestrial frogs and salamanders passing through the larval stage within the egg—with features of typically aquatic larvae—but hatch ready for life on land; and the appearance of gill-like structures (pharyngeal arch) in vertebrate embryo development. Note that in fish, the arches continue to develop as branchial arches while in humans, for example, they give rise to a variety of structures within the head and neck."
2. "Pentadactyl limb - The pattern of limb bones called pentadactyl limb is an example of homologous structures (Fig. 5d). It is found in all classes of tetrapods (i.e. from amphibians to mammals). It can even be traced back to the fins of certain fossil fishes from which the first amphibians evolved such as tiktaalik. The limb has a single proximal bone (humerus), two distal bones (radius and ulna), a series of carpals (wrist bones), followed by five series of metacarpals (palm bones) and phalanges (digits). Throughout the tetrapods, the fundamental structures of pentadactyl limbs are the same, indicating that they originated from a common ancestor. But in the course of evolution, these fundamental structures have been modified. They have become superficially different and unrelated structures to serve different functions in adaptation to different environments and modes of life. This phenomenon is shown in the forelimbs of mammals. For example:
In the monkey, the forelimbs are much elongated to form a grasping hand for climbing and swinging among trees.
In the pig, the first digit is lost, and the second and fifth digits are reduced. The remaining two digits are longer and stouter than the rest and bear a hoof for supporting the body.
In the horse, the forelimbs are adapted for support and running by great elongation of the third digit bearing a hoof.
The mole has a pair of short, spade-like forelimbs for burrowing.
The anteater uses its enlarged third digit for tearing down ant hills and termite nests.
In the whale, the forelimbs become flippers for steering and maintaining equilibrium during swimming.
In the bat, the forelimbs have turned into wings for flying by great elongation of four digits, while the hook-like first digit remains free for hanging from trees."
3. "Recurrent laryngeal nerve -The recurrent laryngeal nerve is a fourth branch of the vagus nerve, which is a cranial nerve. In mammals, its path is unusually long. As a part of the vagus nerve, it comes from the brain, passes through the neck down to heart, rounds the dorsal aorta and returns up to the larynx, again through the neck.
This path is suboptimal even for humans, but for giraffes it becomes even more suboptimal. Due to the lengths of their necks, the recurrent laryngeal nerve may be up to 4m long (13 ft), despite its optimal route being a distance of just several inches.
The indirect route of this nerve is the result of evolution of mammals from fish, which had no neck and had a relatively short nerve that innervated one gill slit and passed near the gill arch. Since then, the gill it innervated has become the larynx and the gill arch has become the dorsal aorta in mammals."
4. "Transition from fish to amphibians - Prior to 2004, paleontologists had found fossils of amphibians with necks, ears, and four legs, in rock no older than 365 million years old. In rocks more than 385 million years old they could only find fish, without these amphibian characteristics. Evolutionary theory predicted that since amphibians evolved from fish, an intermediate form should be found in rock dated between 365 and 385 million years ago. Such an intermediate form should have many fish-like characteristics, conserved from 385 million years ago or more, but also have many amphibian characteristics as well. In 2004, an expedition to islands in the Canadian arctic searching specifically for this fossil form in rocks that were 375 million years old discovered fossils of Tiktaalik. Some years later, however, scientists in Poland found evidence of fossilized tetrapod tracks predating Tiktaalik."
I understand the diagram perfectly, it is (after all) my field. In the bone morphogenetic cladogram the common ancestors would be found at intersections. But that is not what the illustration is designed to show. If you trace fish back through where they join the human line to humans then the total distance covered is representative of the distance of the relationship. The fact that the common ancestor, the organism that existed at the intersection of the two lines, was a fish, is not displayed on the cladogram, for it is assumed that no one using the cladogram would not already know that, just as any fool is expected to know that at the intersection of the mammal and the reptile the common ancestor was reptile. You are tripping on baby steps.
stcordova wrote:
We have no idea what they may give rise to in the future. I think it unlikely that they will give rise to anything closely resembling today's Primates,
So why would have expected them to give rise to primates in the first place.
We had no expectation, evolution is a stochastic process and while we are rather good at seeing what has occurred in the past, a lack of being able to see the exact niche spaces of the future makes it a descriptive rather than a predictive science, at least in a "what's there gonna be" way.
stcordova wrote:
Fish give rise to fish, mammals to mammals. That is confirmed both at the morphological anatomical level and the DNA.
Extant DNA does not indicate we evolved from fish. Not at all.
Ah, that's where you are wrong, it does! See: Mallatt, J., and J. Sullivan. 1998. (1998). "28S and 18S ribosomal DNA sequences support the monophyly of lampreys and hagfishes". Molecular Biology and Evolution 15 (12): 1706–1718; DeLarbre Christiane ; Gallut Cyril ; Barriel Veronique ; Janvier Philippe ; Gachelin Gabriel (2002). "Complete mitochondrial DNA of the hagfish, Eptatretus burgeri: The comparative analysis of mitochondrial DNA sequences strongly supports the cyclostome monophyly". Molecular Phylogenetics & Evolution 22 (2): 184–192; "The African coelacanth genome provides insights into tetrapod evolution "Chris T. Amemiya, et.al. Nature 496, 311–316 (18 April 2013).