Are feathers highly specialized fur?

Not at all. Hair is made of alpha keratin. Feathers is made of beta keratin, and feathers evolved from reptilian scales, which is also beta keratin, although the kind of beta keratin found in feathers is a special kind and it is not found in reptiles. Hair evolved first as whiskers on the snouts of nocturnal therapsid reptiles and mammals evolved from a therapsid reptile. The whiskers allowed these nocturnal reptiles to feel their way around in dim light Later a mutation resulted in these whiskers appearing all over the body of the earliest mammals. As a result, each piece of hair still has a nerve attached to it, even though there is no reason to have nerve endings on hair over most of the body. 

In contrast, feathers evolved first as large solid sheets for Longisquama, an archosaurian reptile,  to glide around. Only later did feathers evolved to have rachis and vanes that are connected to each other to save weight. Longisquama's feathers have many anatomical and developmental similarities to avian feathers, and it is extremely unlikely that such similarities evolved independently in birds and in Longisquama. A more likely explanation is that avian feathers evolved from Longisquama feathers. Further, the most primitive birds, such as Archaeopteryx, were cold-blooded. So too were the enantiornithine birds that dominated the age of dinosaurs on land but were wiped out completely by the giant meteor that wiped out the dinosaurs. Hence the idea that feathers evolved initially as insulation on warm blooded dinosaurs is just plain BS. 

The enantiornithine birds and Archaeopteryx have growth rings in their long bones, and so do dinosaurs and modern reptiles like crocodiles and lizards. Warm-bloodedness only evolved in the ornithurine birds (aka modern birds), which lived in shoreline habitats during the age of dinosaurs. All living birds are warm blooded because their ancestor were shorebirds that escaped the end of the Cretaceous extinction by being able to stay cool in or near the water, when land temperature was oven-like after the giant meteor stuck the earth 65 million years ago. Mammals also survived because many of them lived underground as shrew-like animals and being underground saved from from being fried because temperature underground is cool since heat rises. 

Hair and feathers evolved independently of each other and that is why they share almost no homologous similarities. Some feathers do resemble hair but they evolved to be that way from  contour feathers. Feathers did not evolve from hair-like fibers. 

Feathers are more like scales than fur.  But they are all made of basically the same stuff.  

Feathers are modified reptile scales.

Words mean what people use them to mean. The fact that you put it in quotes shows that you know people don't think of feathers as being fur. But equally you are choosing to concentrate on an aspect of feathers that is like an aspect of fur, so to that extent it is fair game imho as long that remain clear, and as long as you understand a pedant biologist will argue with you all day.

No. Birds?are a totally different class from mammals. Birds?are modern dinosaurs. 

https://www.activewild.com/is-a-bird-a-mammal/#:~:...