Do you know also who first made them?

1894 German toy company Gebrüder Sussenguth show a stuffed bear toy in their catalogue. 1897 Bear skittles and ‘roly-poly’ toy bears feature in the Steiff catalogue and the Steiff company takes its own stand at the Leipzig toy fair. 1899 Margarete Steiff registers patents for 23 of her soft toy designs, including a dancing bear and a bear handler with a brown bear.

http://en.wikipedia.org/wiki/Teddy_bear#Naming

When was the first "stuffed animal" made?

The first commercial concern to create stuffed toys is apparently the Steiff company that was founded in 1880 in Germany. In colloquial German, stuffed animals are often referred as Steifftiere, which derives from the name of that company.

http://en.wikipedia.org/wiki/Stuffed_animal