Someone did say that, but not gladiators. It comes from Suetonius's "Life of the Twelve Ceasar". A group of prisonner is supposed to have said that to Claudius, the fourth roman emperor, during a naumachy (a fake naval battle, in wich prisonners, sentenced to death, were used as foot soldier). There is no mention of that phrase ("Morituri te salutant", litteraly "Those who are going to die salute you") outside Suetonius, so it is generaly accepted that it was not a ritual salute. There is not even a record of a gladiator actually saying anything like it. It is only much more later that this sentence became popular and was wildly used in representations of gladiators.

For the wild beast,yes, but not always, and not every gladiator. Gladiators were elite slaves, specially trained and therefore, very expensive. Throwing them to the lions wouldn't have been a good business practice. Specially trained gladiators, the bestiarii, would fight beasts, sometime lions, but also boars, hyena or wolves, armed with a spear, and assisted by archers (the venatii). It was more a staged hunt than a real fight. The real fight was when prisonners sentenced to death were send to die by the beasts. Sometime they were unarmed and just send in the arena to die, sometime they were given weapons to fight, so the execution would be a little more interesting to watch.