There is no reason for the past tense, the Czech sentence is in the present tense.
In english the "to" marking the infinitive should always be inseparable with the verb
What? A rule in English that is not unbreakable? Impossible xD but seriously, I hope the error will be fixed eventually. That "correct" translation sounds just ridiculous
No, it is not an error. Or if it is, then not just because of the split infinitive but because of something else. Please read the link.