I'm not sure, but I think hög usually refers to the general height of some object, while lång either lefers to a distance/length or the tallness of a person. Just as you wouldn't tell a person "you're very high", because it either means said person is on drugs or is positioned on elevated terrain.
There's some component about things that are called hög that makes them feel like possible landmarks. Since a person typically moves around a lot and doesn't even stand up 24/7, it would be odd to use a word as hög – they're the same "height" when they're lying down, you know! :D
And as you say, if we do say hög about a person, we mean that they're high on drugs. En hög tjänsteman 'a high official' (official as in e.g. civil servant) is somewhat ambiguous though, it could also mean someone high up in the hierarchy :)
No, I'd just take that to be like han står högt upp, that he is standing in a high place. stands tall is an idiom in English that I'm not quite sure how to translate into Swedish – it's more often used figuratively anyway, isn't it? 'be proud and confident' seems to be a common definition.
In some cases you could probably use some variant of sträcka på sig (lit 'stretch oneself'), at least in the imperative. Stand tall! could be Sträck på dig!
står högt can also refer to some kind of hierarchy or value, like dollarn står högt nu means that the dollar is strong.
Come to think of it, you are right that it is mostly used idiomatically, though I was actually thinking about it in literal terms when I asked, in the sense of "he is very tall and towers over people" which actually may be idiomatic, I'm not sure, although definitely less so than the other meaning.
The thing is that the word hus in Swedish is used for a lot of structures that would never be called 'houses' by native English speakers. To them, 'a house' is mainly what we'd call ett enfamiljshus. It's a very common error among Swedes to call buildings 'houses' in English. We also use the word byggnad a lot less than they do in English, so that it's very natural in Swedish to say ett högt hus rather than en hög byggnad.
Of course byggnaden is also an accepted answer when translating this sentence from English into Swedish and it may show up in multiple choice questions.