It's so grammatically so hard for native speaker.
1.안나가 알레크스를 좋아하는 줄 알아요"
Actually no.1 is worng sentence. 은/는 줄 알다/모르다 only can use with past tense.
I don't know how can i explain that. But It's kind of feeling.
은/는 줄 알다/ 모르다 means, For example, I like A. But you think I like B. Someday we talk about that. I say 'I like A'. You say, 'Reall? I thought you like B!!' In this situation, We can use 은/는 줄 알다/ 모르다.
I say, 나는 A를 좋아해요. You say, 정말요? 저는 당신이 B를 좋아하는 줄 알았어요!
Can you understand that? You 'knew' wrong information.
But no.2 always can use. 은/는 것 알다/모르다.
For example, In above situation I like A, You knew I like A.
I say, I like A. You say, I know that.
I say, 저는 A를 좋아해요. You say, 저는 당신이 A를 좋아하는 것을 알고 있었어요.
Also you can use present.
Sorry, My English is so awkward. If you don't understand, Feel free to tell me.
If you can understand some korean, and you have a Skype, We can talk on Skype.