Well,when the mother bear was crushed under the rock i think that it was a mechanical bearI hope that it was fake!

None of the Bear were mechanicals. The Kodiak bear name Kaar, who played the big bear in the movies, was invited as a guest in a French TV show sometimes after the movies. For the smaller bears, they used two of them with a good trainer. If you watch the making of the movies, you will see it all. Try to get the DVD.

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some parts were stop motion animation

I think thats the point in their dreams that is.
M:What are you eating?
B:It's some sort of delicious biscuit!
M:It's a coaster.

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I'm pretty sure they are mechanical bears in the cub's second dream sequence. They look pretty fake, almost like claymation.
"I'm throwin' rocks tonight!"

Yes there were. All the kill scenes were animatronic animals

Hey, even bears have mood swings, especially when he's supposed to do something that was not in his contract
I heard that Youk and Bart got really upset about all the nudity required of them in the film.

The bear death scene from rocks, and also the scene where the cub is standing up trying to get the attention from the adult male bear have bear puppets.
Also, some human sounds were mixed in for the cub's sounds, but it's true that a crying cub sounds very close to a crying human infant.

There were. Jim Henson's Creature Shop built a few minor ones, particularly for the death scene and a few parts (its hard to tell which ones) where a real bear could not be used or was indisposed or had a tantrum and locked himself in his trailer. Hey, even bears have mood swings, especially when he's supposed to do something that was not in his contract, or some animal-rights group felt it was inhuman (I thought we're talking bear?). But it should be noted that Bart The Bear really did most of his own scenes, as did Youk.

I'm afraid there were no mechanical bears in this movie. 90% sure!

I was just watching it with my nephew and I thought that same thing. I think that they had someone loop in more human-like sounds. But I think that they always used a real bear.