I completely agree.
"The taxi is already near the hotel" is something I could say on the phone form the taxi, on my way to a rendezvous at the hotel, or else looking at my phone app tracking the taxi arrival in real time. Both the Russian sentence and your suggested translation rule this scenario out.
AFAIK, cars don't "stand" in English - that's a literal translation from Russian. Curiously enough, in English they "sit": "The taxi is sitting ...", although in this particular sentence it's not needed. Either simply "is" or "is waiting" would be the best translations.
The sentence is correct as Duolingo has presented it.
Because of возле, гостиница must become genitive singular: гостиницы. Genitive singular гостиницы just happens to match nominative plural. :) That is actually one of the nice things about regular feminine nouns - nominative plural and genitive singular match forms.
Genitive plural is гостиниц.
Which part of your sentence implies that the taxi is stationary, and is not merely approaching the hotel? The Russian original is unambiguous about it.
FYI: "The taxi is already at the hotel" is accepted. So are "The taxi is already waiting/standing by/nearby the hotel."
This sentence, "Такси уже стоит возле гостиницы," refers to singular taxi instead of plural taxis. Thus, we would say, "A taxi is..." or "The taxi is...."
Granted, in Russian, такси is non-declinable - which means that whether I was referring to multiple or singular taxis, I would always use the word такси. See declension table here. However, if there were multiple такси, then I suspect I would use the word стоят - see conjugation table here. Он/такси стоит, while они/такси стоят.
You are correct. See https://en.wiktionary.org/wiki/%D0%B3%D0%BE%D1%81%D1%82%D0%B8%D0%BD%D0%B8%D1%86%D0%B0 for confirmation.
However, возле takes genitive, which is the same as the nominative plural....
From this discussion page which we are on, I hear гостиницы. You may indeed have heard some questionable audio on some of the exercises - it happens. If you plainly hear -ца instead of -цы, I recommend that you report the audio as incorrect.
Actually, it can be either, depending on the rest of the sentence. https://en.wiktionary.org/wiki/%D0%B3%D0%BE%D1%81%D1%82%D0%B8%D0%BD%D0%B8%D1%86%D0%B0 shows that it's genitive singular, or a couple of plural options.
In this case, https://en.wiktionary.org/wiki/%D0%B2%D0%BE%D0%B7%D0%BB%D0%B5 shows that "возле" needs the genitive case, so it's just one hotel here.
Quite! See https://en.wiktionary.org/wiki/%D0%B2%D0%BE%D0%B7%D0%BB%D0%B5 for confirmation, if any be needed....
My assumption is that Duolingo is using regular expressions to match our free-form inputs for scoring. I've wondered about the course authors' view before: it wouldn't be fun to enter all alternatives in one giant regular expression but it would be mean beyond belief to not provide a way to input regular expressions at all (ie require every allowed alternative to be listed directly).
For this sentence I would expect the regular expression to look like, at least in part:
^the (taxi|cab) is already (near|by|at) the hotel$ ^the (taxi|cab) is (near|at|by) the hotel already$
And so on.
When a user submits a new suggested translation there is probably an interface for "add this specific sentence" and probably a way to edit the regular expressions directly.
It's inevitable that less-common words won't be accepted everywhere. If you're sure of your translations then hit the report button. Sometimes my suggestions are accepted the next day and sometimes it's months later.