I'm not sure if this is right. "Высоко" is an adverb, but we need an adjective here: высока(я).
Как высока́ эта гора?
But I suppose it's much more common to say: Какая высота (у) этой горы? / Какой высоты эта гора?
For the adverb: Как высоко расположена вершина этой горы.
I'm not an expert in the other two languages, but I don't think the adverb works there either.
'High' is one of those words in English, which don't have a separate adverb form (like fast, hard, low...). In this particular sentence it modifies a noun, which makes it an adjective. In other contexts, where it modifies other parts of speech, it is an adverb. For example:
How high can you jump? - Как высоко ты умеешь прыгать?
Both wysoka and high are hence adjectives in this exercise and I see no reason why East Slavic languages would make an exception and allow an adverb here. Высока may be literary, but it's at least correct and it's even more similar to wysoka than its corresponding adverb.
The preferred answer should be "How high is this mountain". I have never heard anyone refer to a mountain as being "tall" — until now!
A building can be regarded as being "tall" because its height usually exceeds its width. There are mountains (Mount Fuji, for example) whose widths exceed their heights — so they should be called "high" rather than "tall".
Please refer to: https://pediaa.com/difference-between-high-and-tall/
Well, it's not accepted and it will probably stay this way, even though I could find some examples in the corpus. Maybe it's a regional thing, or just inferior style, not sure.
It definitely works as statement, though: Spójrz, jaka wysoka jest ta góra! - Look how tall this montain is!