Hope requires a strong self to mediate between our ideals and our desires. So if Buddhism says the self is an illusion, it can only lead to the acceptance, even the valorisation, of fate.
If we give up our self, we are left without agency, we know we are left without control, and left to fate.
Not necessarily. Buddhism says we should let go of the self in order to see reality as it is, and only when we see reality as it is we are able to change it, or keep it the same, if that's what we decide.
I don't believe it's an illusion, more of an abstract concept.