Was there ever a bear called the cave bear?

Answer 1

Yes.

The cave bear (Ursus spelaeus) was a species of bear that lived in Europe during the Pleistocene and became extinct at the beginning of the Last Glacial Maximum about 27,500 years ago. Both the name caveand the scientific name spelaeusderive from the fact that fossils of this species were mostly found in caves, indicating that this species spent more time in caves than the brown bear, which only uses caves for hibernation. Consequently, in the course of time, whole layers of bones, almost entirely those of skeletons, were found in many caves.

Answer 2

Yes, there were bears during the ice age.