"He will be teaching at school."
Translation:On będzie uczył w szkole.
Polish does that a lot, this sound-changing. With ł-l it happens in dative and locative, so that's why you have for example:
szkoła -> o szkole (school)
pszczoła -> o pszczole (bee)
jemioła -> o jemiole (mistletoe)
piła -> o pile (a saw)
kiła -> o kile (syphilis)
I guess that probably happens always with "-ła" endings of nouns, but I cannot guarantee that.
That also kinda explains przedszkole (kindergarten), even it it's not exactly the cases that are the case here.
So there are two correct options "On będzie uczyć w szkole., On będzie uczył w szkole."
Yet if I use the infinitive in other questions they are wrong?
I would have to know what exact questions you mean. But apart from modal verbs, I think everything else should be able to use infinitive when we use Future Compound.
why sometimes the translation of this future is "I will go to school" and sometimes "I will be going to school"?
But this sentence is not about going... I'd say that your sentences are different in Polish, "I will go to school" = "Pójdę do szkoły" and "I will be going to school" = "Będę szedł/szła/iść do szkoły".
Oh wait. Maybe rather: they can be different in Polish. 'Cause English and Polish don't correspond as well here as it seems at first sight. We could say that "I will be going to school" focuses on the process, so it translates into Future Compound (Będę szedł/szła/iść). But I guess that "Pójdę" is not exactly a wrong translation.