C.
The conclusion is that dinosaurs are closely related to birds. The evidence to support this conclusion is that TRex bones collagen tissue is similar to that found in birds.
One thing that jumps right off is that the evidence is for a single species of dinosaur i.e. TRex and a generalization has been made that all dinosaurs are related to birds.(A) How rare it is to find preserved soft tissue in the bones of a dinosaur?
The possibility of finding the tissue is rare or not has no bearing on the conclusion whether the dinosaur is related to birds or not.
(B) Is there any evidence at all against the claim that dinosaurs are closely related to birds?
One evidence the author himself cites to claim that dinosaurs are related to birds. Also, if any other evidence exists against this claim, we don't know for sure about the validity of conclusion. This would further require us to make many assumptions.
(C) How likely is it for animals that are not closely related to each other to have similar collagen proteins?Exactly. If its very common that two animals can have collagen, this weakens our claim since even lions for that matter could've similar collagen but clearly they ain't birds. If it's not common, then our conclusion is strengthened.
(D) Is it possible that T. rex is more closely related to modern-day chickens than to certain other types of dinosaurs?
Relatability between two species of dinosaurs is irrelevant.
(E) Before Schweitzer's discovery, did researchers suppose that the collagen proteins in T. rex and chickens might be similar?
What researchers supposed, believed etc. before making discovery/while making discovery is out of question. the outcome of their research is being spoken about.