The storage chest in the battle tower is along the left wall as you enter the master's chamber, beside the bed (at the back of the throne room, take the elevator down). There are a couple pieces of dragon equipment you'll probably want to use in there.
If you fly out over the water from the start of the fjords, you should see a bunker high in the mountains behind some anti-dragon shields and defences. That is where you need to get to lower the barrier and disable the shields (there are a couple traders in there, as well, after they surrender).
You can either use a teleporter to get up there (the Camp Sentinel View teleporter, on the west side of the island in the middle of the channel, on a ledge directly above the left Nest Tower as you approach the cliff, will bring you to Camp Eagle's Nest, where you can access the bunker) or it is also possible to fly above the anti-dragon shield and drop down in human form, if you find the right spot.
For the last two platforms in the depleted ore mine I think I just jumped from behind the lever used to trigger them, after initially trying to stand on the edge of the platform, hit the lever and jump backwards onto the first platform to theoretically save some time jumping forward to the second platform. IIRC it was easier to just face where the platforms would appear, jump forward, turn and jump again (you can pause the game as you land to rotate the camera direction, and make the second jump faster).
In another topic describing my playthrough I mentioned getting an elder class helmet out of that chest, which was a slight upgrade to the one I had been using (I cleared the mine of opponents earlier, and left the book and platform puzzles, as well as malachite veins, until I was level 35, just not getting back until I started clearing up stuff getting ready to head to the Hall of Echoes). If you can't get the jumps in a reasonable amount of time, then you don't have to worry about just skipping it.
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