AFTER Г, К, Х, Ш, Щ, Ж, Ч, WRITE И NOT Ы -- 7-lettter

AFTER Ш, Щ, Ж, Ч, Ц, DO NOT WRITE UNSTRESSED O, WRITE Е INSTEAD -- 5-letter

Isn't по-русски used only for non-action verbs like "to know" rather than "to speak"? I might be confusing the two, but I know our teacher said that по-русски is used in conjuntion with some verbs while русском языке / Русский язык is used with another set of verbs.

Thank you, though, for the correction. It makes more sense, I think.