You can't normally use 'koibito' for someone you have unrequited love for. But, I guess you could think that to yourself (regardless of what the other person thinks).
'[My] screen koibito' (an example of one-sided usage) isn't a typically used expression. It's a little hard to understand, but I think it would mean what you thought, that someone is thinking of a film actor like that on their own.
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'Koibito' is Japanese, so I think it shouldn't be compared with other languages. (Re; 'can koibito be used like "you're such a sweetheart/etc"'
'Koibito' in Japanese:
1) Refers to people.
2) Refers to the object (other person) who the subject is in love with. Also, the other person must concurrently also love the subject. In other words, it is 'the other person, where the subject and other person both love each other'.
Example:
He is my koibito.
= I am in love with him, and he is also in love with me.
I am in love with him, but he is not in love with me.
=/= He is my koibito.
You can't use it like this normally.
3) It it also used to refer to that relationship.
Ex: We are koibito.
4) But, 'koi' is passion which can be influenced by emotions, so the expression 'koibito' is based on the subjectivity of the speaker.
We are koibito. (The speaker might think this, but you don't know if the other person agrees or not.)
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"Can 'koibito' be taken as meaning 'she's a kind-hearted person, everyone loves her, she's very popular, etc'?"
No, it cannot.
('Nihon no koibito/Japan's Sweetheart'
is strange Japanese.