It is not uncommon to hear someone say that is a high mountain or hill. For a building it would be tall and not high usually
I translated "... egy kórház" by "... one hospital" and got corrected. I thought since egy = one (the numeral), it could be used in this context. Is there a reason it's not possible here?
When I learnt basic English, told me that tall is for people and high for things.
I think that was just a sort-of-useful approximation. What's important is to not use "high" by itself for people unless you mean they are under the effects of (illegal, generally) drugs. As a native English speaker, "high" is not used to describe heights of things. It's used for "elevations," above either the ground, floor, or sea level depending on context.
Not always. But people are only high if the are far up in the mountain, hill, tree, in a building. The person is high in the “. “. Or high on drugs ; almost always illegal drugs