Yes
Yes
The English name for this bird is the Northern Three-Toed Woodpecker.
This beautiful bird is far wider spread than one would expect.
This is apparent from it's full name :- "Eurasian Three-toed Woodpecker".
They are to be found anywhere between Norway and Korea, Also in North America and Canada.
See link below.
It depends on which species you are talking about. There are four species of three-toed sloth.
Three toed sloths are not extinct.