While I understand that "high" is not a good term for people, I think it should be accepted for trees.
'Tall tree' is preferred in English.
Could this also mean ‘high’?
Yes, "vysoký" in Czech is used both for "high" and "tall".
Is "vysoké" used here (instead of "vysoká" or "vysocí") because "stromy" is masculine inanimate? Or am I missing something?
Yes, it is because of that.
These versus those? Is there another Czech demonstrative which makes this distinction? Can not ty be translated by either?
ty/tamty/tamhlety vs tyto/tyhle/tyhlety
The translation says that "these" trees is incorrect. Unless there is context, how can one say that "ty" cannot mean "these"?
See above. It just is not the meaning of that word.