If the T-Rex is the ancestor of Chickens, then is the Spinosaurus the ancestor of Ducks????

T-Rex is NOT the ancestor of chickens, nor of any other bird, and no scientist ever said it is. It is creationists who make up that false statement in their attempts to refute evolution.

T-Rex was a theropod dinosaur, which comprises a very large group of dinosaurs, from quite large to small types. The fossil evidence indicates that birds evolved from  a small, feathered theropod dinosaur.

It is now clear from their bone structure from the fossil evidence that at least some branches of the dinosaurs were warm blooded and much more active than their reptilian ancestors. Numerous examples from the fossil record also show that many of these dinosaurs had evolved feathers, which would have originally been used for insulation. From that initial use other uses would have arisen, such as for camouflage or elongated for sexual display. Some of the smaller tree-climbing feathered theropod dinosaurs began using their elongated feathers on their arms for gliding. Eventually, they evolved into powered flyers.

The earliest example of such feathered, winged dinosaurs was that of Archaeopteryx, which was first found in the 1800s. See the image below for one of those fossils. It also shows its skeleton in relation to modern-type birds. It is clear that the skeleton is still more like that of a theropod dinosaur than like that of a modern bird, including having teeth, a long bony tail, and separate forelimb digits with claws instead of the fused digits of modern type birds.

Fossils of numerous other small, feathered, dinosaurs, including winged, have been found in the past thirty years, enough to make it clear that birds descended from a feathered theropod dinosaur.

See the video below for a couple of other examples of that type of dinosaur.

https://www.youtube.com/watch?v=-fyxUxGdrns

These early ancestors of birds first arose over 150 million years ago and gradually evolved into modern-type birds before the end of the Cretaceous (which marks the demise of the non-avian dinosaurs) but present-day species do not appear in the fossil record until in strata laid down much later during the Cretaceous.

You can ignore @CRR's link. It is typical creationist misrepresentation of facts. Incidentally, the "ducks" in that link are not pf present-day species of ducks. Fossils of what could be the early ancestors of ducks have been found in late Cretaceous strata, though they could also be not related to ducks bur rather an example of convergent evolution via adaptation to a similar ecological niche..

[edit] Dr Werner: “Museums do not show you these modern bird fossils nor do they put modern birds fleshed out with feathers in their dinosaur dioramas. This is wrong. Essentially, every time you see a T. rex or a Triceratops in a museum display, you should also see ducks, loons, flamingos or some of these other modern birds that have been found in the same rock layers as these dinosaurs, but this is not the case. I have never seen a duck with a dinosaur at a natural history museum, have you? An owl? A parrot?” [/edit]

We don't think of a duck flying overhead as T Rex stalked the earth but that is what the fossils show us.

If I remember my course in symbolic logic, when you start an IF-THEN statement with a false statement, you can end it with either a true or false statement and the whole statement will be valid either way. So, the answer to your question is yes.

I don't believe so. I know that the closest relatives of Spinosaurus were Suchomimus ("crocodile mimic") and Irritator (species named that way because Paleontologists were frustrated with it being tampered with).