Translation:Let's go to another store.
Does anyone know the history of the way the Japanese imported this? I ask, because 他 in Chinese means "he." In Chinese, it always refers to a person. I suspect the original always meant person, especially because of the danrenpang (单人旁)- the "jin" 人on the left side of the character, but I don't know the actual historical use of the word.
I'm curious about this as well. Looking up the character it has the person radical and then the component 也 a classical kanji for "to be". So it referring to a person makes perfect sense.
While the components of kanji often don't hold so much weight in meaning, Jisho also lists 化 "change" as a component; which may be where the 'otherness' aspect comes into play?
Looking up the etymology "other, another" does seem to be a secondary meaning in Chinese as well, so somewhere along the timeline japanese switched its primary use.
In Chinese, 也 is ye, "also." So, the two radicals together translate as also person, i.e., "he." For a lot of other related words, I've found that the way the Japanese do things is the way Chinese USED to do things. Examples are 犬 (Japanese inu-dog), and 先生 (Japanese sensei- teacher). Those were the words for dog and teacher in at least one of the Chinese dynasties, but have since been supplanted by the modern 狗 (gou) and 老师 (laoshi) respectively. 犬 is no longer used, and 先生 now means Mister . 他 doesn't fit that mold though. In ancient China, 他 meant he, she, or it. Nowadays, we have 3 words for those 他，她，and 它。All pronounced ta.
Kind of like how the French spoken in Montreal, Canada is closer to the historical French than the French spoken in Paris. There's an error in another Duolingo exercise, where they translate sensei as Mister. It is an odd mistake, unless the person who set the exercise up knows some Chinese.
That's really interesting that 先生 means Mister now. In english it'd be unusual to call your teacher "teacher -name-" so as far as titles it's more common to call your teachers "Mr./Mrs. -name-", so being used when attached to names the mister translation would make sense with the profession more implied in english. That could be what Duo was trying to teach, and the character also happening to have that meaning in Chinese could just be a nice coincidence. Still odd though if it's stand-alone translated that way, it should be listed more as a secondary translation than a primary one for japanese.
In Japanese, the use of honorifics (e.g., -san, -kun, -sempai) is very common, and is essentially mandatory when speaking to someone else. This is unlike in English, where we normally omit the honorific. In the example I am referring to, Duo wants you to translate an English sentence that went "Mr. Tanaka..." It marks Tanaka-san as wrong, but Tanaka-sensei as correct.
In Japanese, sensei is used as an honorific when attached to someone who is teaching you(who may not be a professional teacher). But the sentence itself provided no such context- it asked for Mr. Tanaka, not Teacher Tanaka.
In Chinese, however, if you had said Tanaka xiansheng (The Mandarin equivalent), that would have been correct grammar.
When I read a Japanese sentence, I half-read Japanese and half-read Chinese. This is partly because I can never figure out which of 5 different Japanese pronunciations the word is supposed to use (is 人 jin, rin, hito? Who cares, just read it as ren (the Chinese)- I know the meaning. It has something to do with a person!). I wouldn't be surprised if the person who created the erroneous answer did the same.
-しょう is an ending used to express volitional form (basically when you want to do something). So the English equivalent is "let's do/eat/go/play etc..."
Typically you chop off the verb ending and add "よう" or just "う". Examples:
食べる --> 食べよう 行く--> 行こう notice for this, and for most う verbs, we had to change く to it's corresponding "o" sound which would be こ。
Exceptions are: する--> しょう 来る--> こよう。
する's volitional form is what you are seeing there.
I agree with your explation of (informal) volitional form but I think that your last sentence may sets some confusion. What he and all are seeing there, in the sentence「ほかの店に行きましょう」is not really the volitional form of する「しょう」but the polite volitional form.
That is, to get a verb in polite volitional form you pick up the dictionary form and transform it into the stem form + ます; so that you get ます-form. Then just transform ます to ましょう.
For this case: 行く(dictionary form) --> 行き+ます --> 行きます (polite positive non-past tense) --> 行きましょう (polite volitional form)
の as possession is correct but could mislead. Thing of it as an "adjective-fyer" particle. It makes the preceding word an adjective.
Let us take a familiar example: 私のお母さん you know that the no indicate a possession so this sentence means my mother. But you can also thing the 私の part as "the adjective form of 私" which is the possessive adjective equivalent to "my" in English. The の particle means that the preceding modifies what comes after the particle.
Now, how to know if a word is の, な, or い adjective?
い adjective is the pure adjective.
な is an adjectival noun. Without な it is a noun form of that adjective. Example: きれい「な」meaning beauty without な and beautiful with it. 好き「な」meaning fondness/likeness without な and favourite with it.
の on the other hand is pure noun. The possibility is endless. You may have seen one in the colour section such as 緑色の「みどりいろの」meaning green as an adjective.