I don't know how people announce these things to the elders, nor what happens if the elders don't agree.
There's no announcement. One simply partakes of the bread and wine at the Memorial. If the elders don't agree, tough for them, it's not for them to decide. According to JW theology, it is a personal matter that God reveals to the individual. That doesn't mean the elders might not make life difficult for the person if they disagree, but it would have to be in other ways, not because of the person's profession of anointing.
Which is more prestigious? Being an elder or being a member of the heavenly class?
Probably being an elder. It certainly carries more power and influence, especially since the "new light" about the F&DS
Are there cases where someone declares and then is badmouthed by members in the congregation?
Probably, since JWs will bad-mouth anybody in the congregation who's different. But I'm not personally familiar with any instances,
I understand declaring when you're not really a member of that class is a serious sin. If you do everything else right, but are wrong about that, would Jehovah forgive you? Or would you forfeit your resurrection?
According to their theology, one who partakes unworthily eats and drinks his own destruction. They understand "partaking unworthily" to mean partaking if one is not truly anointed. Obviously, if one does this deliberately, there would be little hope unless he or she repented before Armageddon.
Finally, after becoming a Jehovah's Witness, how long does it take before you're informed that you are of that class? Are we talking days, months or years?
The only one who informs you, according to their understanding is Jehovah through the holy spirit. He can inform you at any time and in any way that he wants. It might be immediately upon baptism, or after many years of faithful service.
Understand that I do not agree with their theology; I'm merely trying to answer your questions as a JW might.