Why does Satan possess certain people himself rather than send his demons, and is possession by Satan personally rare?

We do not have firm answers to a lot of this, but a few things can be said. Satan cannot divide himself into two or three or four; he is one entity, which is exactly why he has minions, because he cannot be everywhere at once. Only God, being divine, can be everywhere at any time, so Satan has real limitations. Possession by Satan personally is going to be very rare. When a movie claims a demon says, 'I am Satan, I was in Hitler, in Mussolini, in Judas,' that is Hollywood, and demons will lie about anything, so you have to be careful; a real possession may lie behind the story, but the dramatized details are not to be trusted. The only one we know for certain was possessed by Satan himself is Judas, and we can understand why: it was crucial to get Judas to do what he agreed to do and not change his mind, because the devil thought that killing Jesus would foil God's whole plan and leave the devil victor as in Eden. We might assume that for anyone else as pivotal as Judas, the devil would handle it himself, but we simply do not know who they are, and it is useless, even dangerous, to speculate.