Interestingly, I read that comment before I read the story, and so when the other child appeared for the second time, I was actually wondering whether he was something like an angel and whether the MC would die at the end… But I would not have guessed that without your remark, that’s for sure.
In Japanese, Taro is like the prototypical male character name. So you will see lots of (especially old) stories where a male protagonist will be called Taro. I even found a forum thread on the name 
Today I have some time to point out a few grammar points.
金の輪
In Part 1:
遠くの方まで遊びにいったものとみえます。- it seems like - https://japanesetest4you.com/flashcard/learn-jlpt-n4-grammar-とみえる-to-mieru/
Last sentence of Part 1:
懐かしげに見えました。- seeming, giving the appearance of - https://japanesetest4you.com/flashcard/learn-jlpt-n2-grammar-げ-ge/
Second paragraph of Part 2:
その少年のことを考えました。- How to use Noun + のこと ( = no koto) / のことだから(= no koto dakara) + のことだし( = no koto dashi) – Maggie Sensei
大きなかに
ある日のこと - see above 
これから出てゆこうとしたおじいさん - grandfather who was about to leave - meaning - What is the difference between "verb＋て＋みる" and "verb＋(よ)う+とする"? - Japanese Language Stack Exchange
Btw ゆく is just a different (and I think a bit old-fashioned) spelling for いく, i.e. 行く.
「。。。今夜はお泊まりなさったにちがいない」When reading I took a wrong turn here at first, so I thought it’s worth mentioning that this is not 日がいない but instead に違いない - without doubt
その夜にかぎって - especially / only on that night - https://japanesetest4you.com/flashcard/learn-jlpt-n2-grammar-にかぎって-ni-kagitte/
いつもなら、太郎は日が暮れるとじきに眠るのでしたが - In order to understand why there is a の right in the middle of nowhere, let’s pick the sentence apart a little bit:
いつもなら、太郎は X でしたが - If it were (a) normal (day), Taro would have been X but… . Please keep in mind that the shape of the sentence requires X to be a noun.
日が暮れるとじきに眠る - sleep at the time when the sun sets This is the desired meaning of our X, but as you can see it is not a noun, so we need to attach の in order for this whole sentence to become a noun that can fit into the spot of X in the overall sentence.
この鳥に乗って帰ってきなすったのだ - this is an old form consisting of 来る + なさる, it is polite but the meaning is the same as きた, i.e. “he came home riding on this bird” - Learn Japanese Forum - 来る vs 来なすった
And finally, there is this sentence:
彼は、朝起きると、入り口に、大きな白い羽の、汚れてねずみ色になった、いままでにこんな大きな鳥を見たこともない、鳥の死んだのが、壁板にかかっているのを見てびっくりしました。It was pretty much smooth sailing until now, and all of a sudden we get hit with such a truckload of a sentence (I am convinced that this is a strong stylistic choice, maybe to already indicate that this is not real but actually a dream?) Anyways, let’s look at the contents.
The general structure is this:
彼は、朝起きると、X を見てびっくりしました。- When he got up the next morning, he saw X and was surprised.
This is X:
入り口に、Y が、壁板にかかっているの - a noun (note the trailing の) that describes “at the entrance, Y was hanging from the wall”
Now this is Y:
大きな白い羽の、汚れてねずみ色になった、いままでにこんな大きな鳥を見たこともない、鳥の死んだの - it is a noun that is being described by two properties:
Property 1:
大きな白い羽の、汚れてねずみ色になった - don’t let the comma confuse you, these two parts still belong together. The の before the comma is a case of の as a replacement of が (Replacing が with の | WordReference Forums), so the sentence could be rewritten as 大きな白い羽が汚れてねずみ色になった - the big white feathers were dirty and had turned grey
Property 2:
いままでにこんな大きな鳥を見たこともない - until now [Taro] had never seen such a big bird
Finally, the noun:
鳥の死んだの - in this case, in my opinion the final の serves as a placeholder for an unsaid thing (here most likely something like “body”) - have a look at https://www.imabi.net/theparticlenoii.htm and scroll down to the section labeled “One”. In English this would be “the bird’s corpse” or “the dead bird”
Side discussion:
Interestingly, the word 壁板 - Jisho.org has the furigana しとみ - Jisho.org. This could be an outdated reading? Anyways, I take the overall meaning to be that the house was built of wooden boards or that the outside was coated with wooden boards.