The only correct option is the second one. The first is wrong because 'English' begins with a vowel, so you need to use 'an' rather than 'a' before it. The third is wrong because countries, nationalities and languages always need a capital letter.

Only number two is right. It is 'an English learner.' 'English' starts with a vowel sound and thus we switch to 'an'. Any native speaker will tell you that 'a English' feels horribly unnatural as it is difficult to say two vowel sounds one after the other like that.