Valid question, since given item technically leaves your inventory. I think the intention is that if you ever had to discard that card for any reason, it is banished instead. Thematically it's one of a kind item and cannot be found again (but can be given). I would never banish it while giving/swapping - but I cannot really find an official rule to make this claim bullet-proof.
I was wondering about the 10 days east too at first, but then realized that you cannot go 10 cards straight east from the VG - because there is a river blocking your way. The underground entrance is still directly to the east, but to physically reach it you need to use the bridge, and the shortest path through the bridge takes exactly ten cards. We were satisfied with this explanation and happy we solved it.
But then to "save some time and energy" we decided to use magic (not going to spoil) instead of walking. I just say we overestimated us being able to properly utilize such a powerful item, but it was fun and we recovered eventually ...
We have just reached the cave and don't know about the wheel yet.
Also many people were disappointed by the turtle enigma in the PNP [citation needed]. I have not seen this kind of puzzle in the full game yet - but there are many interesting and solvable ones - so don't be afraid the whole full game will be like that.
Using an action on an item card decreases durability. Rules page 21, top:
A player may use an item in their inventory – by lowering its durability by 1 – either to apply some or all of the the item’s effects [...], or to take an action featured on this item.
) that summons #311 indirectly. You have probably used it already.