Question

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Answer 1

Modern birds require certain climate conditions to live. Scientists assume that these birds’ ancestors also needed those conditions to live. Where fossils of such birds are found, scientists can conclude that the climate conditions required by similar modern birds existed.

Answer 2

Study of the analogy i.e., the convergent evolution of the birds would help in that case. If we study the analogy of the birds, we would be able to know about the environment that they live in. For example, if the birds have the granivorous features,  then it is confirmed that lived in or near a forested environment. The birds or animals, in general, adapt themselves to live in a particular condition or climate, without which they would die. Therefore, typical features of the birds provide information about their habitat. 
When modern and fossil birds have similar features, that means that both birds lived in a similar type of climatic conditions and thus, did not had to change or adapt themselves differently.