I also wonder if the root of the mountain and the bear's sinew are possible to obtain. In case it helps anybody, here are some ideas I've come up with, and a few things I've tried that haven't worked:
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Root:
Thinking of the definition of the word "root," could be
* the base of something
* the source of something
* an actual root (of a plant)
* maybe something that resembles the root of a plant (at least in Eitri's eyes?)
Mountain:
Could be
* an actual mountain that appears in the game (the area where the troll caused the avalanche seems mountainous, Egther's keep looks like it's at the top of a hill, the watchtower is on a cliff, and Svartelheim is underground, so maybe it's under some mountains?).
* a big pile or formation of...something, not necessarily rock...a metaphorical mountain, like a large obstacle or problem, or something that must be ascended or climbed to the top. I suppose you couldn't find a molehill and make a mountain out of it...
* something mountain-like in material...something made from stone/rock/lava?
Combining the "root" and "mountain" ideas, a root of a mountain could be
* something that forms the base of a mountain (a rock or something similar? Gem? Crystal? Lava?)
* something that caused a mountain to form(?)
* the source of a mountain (Midgard is supposedly made from a giant's body, right? I read that the land is made from his flesh and the oceans made from his blood.)
* something that resembles a root but is made of stone (a root or trunk or branch of a petrified tree?)
* an actual plant root that grows at the base of a mountain (The only roots I remember seeing in the game are the banner of the tree in Aurvandell's room, which has the roots as part of the symbol. There are some roots near the gate of Fornsigtuna. And you can get roots from the duergar.)
* something that resembles a root and is near the base of a mountain (coral from Svartelheim? Are these objects definitley supposed to come from Midguard? So, looking for them in Svartelheim would not be useful?)
* Or you could you attach a plant root to a rock, somehow?
* Or "plant" a rock in some soil in a little flower pot, as though you are "growing" a mountain, similar to how Eitri's carrots growing in a pot?
Things I've tried:
Eitri didn't seem interested in coral, or any gems that I remember. I tried clicking the roots on Eitri's caged pet to see if he would turn them to stone, but that didn't work either.
Bear's Sinew:
For the bear's sinew, it seems like the honey might be a good way to attract a bear, but I have no idea where to put it.
After killing the gulon, I tried clicking various weapons on the gulon to see if I could get a sinew, and that didn't work.
Someone else in another thread mentioned a rope maybe resembling a sinew. I've tried cutting the net to make a rope. That didn't work.