They say it was payback for what happened to Piso. Piso was a long time supporter of the Claudians and Sejanus had a role in pressuring Tiberius into having him put on trial for poisoning Germanicus, which was never proven. Piso committed suicide.
Unlikely, although Piso’s father had fought against the 1st triumvirate, against Caesar, and against Octavian, so the son’s activities in the east can be seen as rebellion.
OTOH, the family’s fortunes were restored after the suicide, and his widow was let off the hook.
Sejanus’ rise was well underway when Piso killed himself, but AFAIK there’s no trace of his involvement. Not much later he turned out to be a much more formidable threat. He married into the Claudian family, ultimately had interests that overlapped Tiberius’ own, and took the fall for the reign of terror that to some extent benefitted Tiberius.
Given the backstabbing that went on continually within the Julio-Claudian dynasty, I’m not too sure I’d have tried to climb that particular career ladder.
Antony’s kids with Cleopatra were well-kept and well married after they came under the protection of Augustus after A & C bit the big one. Their family lines seem to have drifted into obscurity in a few generations, which could mean they died out, but of course there isn’t a pristine archive of Roman birth records to consult.
Caesar and Antony were such hounds during military campaigns that it would be astonishing if they don’t have millions of descendants. More specifically, it’s very unlikely that such a line of descent could be proved.