Expedition: general discussions.

In other words, any mage and scholar can steal, but only a warrior can wear chainmail? How realistic.

Only a character with high agility can steal successfully.
Everyone can wear anything and use anything, but there will be penalties. By the way, the scholar needs to have medium armor added.

A very weak bonus, considering that it's essentially equivalent to two or three stat points.

I'll adjust it.

Are there any effects besides healing/resurrection?

Well, stats change depending on the type of animal. What else should there be? Control over the character remains, but in some situations, instincts can take over.

How often will characters have to ride horses?

You only travel between locations on them. In small settlements, you can stay mounted without needing to. It also depends on where you go. In the forest, of course, you can't use horses. In the north, horses will be useful for quite a while (the far north hasn't been explored yet; the northernmost are the Ingelstad, whose climate is similar to the tundra), and in the desert, it all depends on supplies.

Added 2 minutes later
Yes, it's not very significant, so it's an extra stat for them.