'po angielsku', 'po polsku' - are adverbs, because they answer the questions 'how?' or 'what way?' and they are examples of two-words adverbs (adverb phrases).
First word is 'po' and second is an archaic declination of an adjective ending with 'u'. Other examples:
-Chodzę po cichu = I walk quietly
-Czytam po ciemku = I read in darkness
-Robię to po mojemu = I do this my way
-Ta książka jest napisana po angielsku = This book is written in english
As you see in the last example: 'po' stands for 'in'. Sometimes you can replace it with a normal, one-word adverb, for example:
-Chodzę cicho = I walk quietly
but mostly you can't do it, you don't say: 'ta książka jest napisana angielsko'. Some adverbs evolved from two-words to one-word expression. For example:
-Jem pomału = I eat slowly
it's confusing, I know...
I think the issue is that, with Spanish and German, I'd already been studying them for years before I joined Duo. Although I have been exposed to Polish from a young age, I've never studied it and so have zero knowledge or understanding of anything you just said! Once I get to a certain basic level, I may have to do a grammatical course as well.
English - [język] angielski
Speak english - mówić po angielsku. It's dative case, but it's used only in this sentence. In any other sentences you will use dative form "angielskiemu" (like "I gave it for the english boy - dałem to angielskiemu chłopcu"
https://en.wiktionary.org/wiki/angielski - full declension of angielski
(sorry for my English, ;) )