그가 나를 사랑하는지 아닌지 모르겠다. 그가 나를 사랑하는데, 그 사람 엄마가 나를 싫어한다. as you know, these can be translated into as follows. I don't know WHETHER (OR NOT) he loves me. (그가 나를 사랑하는지 아닌지 모르겠다. ) He loves me. BUT, his mother hates me. (그가 나를 사랑하는데, 그 사람 엄마가 나를 싫어한다.) In the former sentence, "~는지 아닌지" takes the role of whether or not. here are two more sentences having the same sentence structure as above. 나는 그가 올지 안올지 모르겠다. ( I dont know whether or not he will come.) 그녀가 넘어질지 안넘어질지 모르겠다. (I dont know whether or not she will fall.) and in the second sentence, 그가 나를 사랑하는데 are made up of the sentence '그가 나를 사랑한다.' and the conjunction, '그런데'. as you may know, 그런데 can be but, however, (and) yet, nevertheless, still, though, now, for all that, by the way or by the by(e) in English depending on the sentences it is used in.

(I may be mistaken) a few weeks ago, you asked about the three word-endings of predicates, which are ~지, ~는데, ~거야. so i will briefly write about them. ~지 can be widely used in affimative sentences such as imperative, interrogative, declarative, and exclamatory. 이제 어서 공부하지. go ahead and study. (imperative) 나도 가지. i will go. (declarative) 그녀는 언제 오시지?/ when does she come? (interrogative) 그는 어떤 사람이지? what kind of person is he? 참 좋지! how nice! (exclamatory) 그는 이름난 효자이지! he is a well-known fillial son! the ending of the word ~데 (which is different from ~데 used above in 사랑하는'데' meaning "but")ends predicates with some sense of exclamation and shows the listeners that the speaker expects some kind of responses from them. 꽤 열심히 공부하는데. (he) works pretty hard! 잘 달리는데. (he) runs really well! 성적이 많이 올랐는데. his score has risen pretty high! the ending '~ㄹ 거야' shows the speaker's subjective conviction, prospect or conjecture. 새 학기에는 정말 열심히 공부할 거야. i will study really hard in the coming semester.(conviction) 이 제품은 틀림없이 인기를 끌 거야. this product will definately be popular.(prospect) 내일은 날씨가 좋을 거야. it(the weather) will be nice tomorrow.(conjecture) i hope the answer somewhat satisfies you.