The verb "uče" is not a participle, but "přechodník přítomný", I do not know how to name it in English, sorry, but the participle means "příčestí" in Czech. We commonly use "příčestí" to form past tense or passive voice. Both "přechodník přítomný" and "přechodník minulý" are nowadays old-fashioned and bookish and we rarely use them. Your sentence with "přechodník přítomný" is correct! You've only missed one comma. ;) "Uče se češtinu s aplikací, poslouchám..." great job! And it is used exactly in the way that you've used it. :)