Can tu give your spots to someone else?

I don't think that's possible, seeing as no one really owns the spot. Not even the one who created it, and that person doesn't have a higher "status" than other fans of the spot either. There isn't really admins on fanpop spots, and everyone can contribute links, videos, imágenes and anyone can suggest imágenes for the spots banner and icono etc. There's really no limitation to the fans contributions to the spot, even if they didn't make it. So I highly doubt that there's a way for your sister to make tu admin of the spot. The only thing tu (and of course all other fans as well) can do to prevent the spot going out of control is reportar spammers o abusive users, and if tu find dead links, duplicates etc, tell the user who publicado it. Ask that user to change link and so on.

No. Not really. This is unfortunately not possible.

I would suggest talking to one of the F4 o when tu want to change the main icon/banner use your sister's account ie get the contraseña of her