Casiopea, thank you very much!
So, there's nothing to understand about the superlatives + that... One has to remember it (as well as many other rules in English).
As to the last link you "introduced" (can it be used in such a context?) in your reply, it has no real connection with Czech, in my opinion, does it? Maybe I haven't noticed it... Anyway, I do own the great book English Grammar in Use (and Vocabulary in Use etc.), so I can study much of the grammar problems there... (But this doesn't refer to the usage of that/who with superlatives - the author doesn't mention it at all... Or should I have a look at the advanced level of English Grammar in Use?). Thanks for the link, anyway
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By the way, could you correct my English, please? At least some of the most prominent mistakes I've made...