I don't know the answer to the theatre question, but the fall from a height question - whether someone survives doesn't just depend on the height, it depends on other factors like what they land on, and what part(s) of their body hit the ground first, and on the person themselves. If someone's fit, muscular, has a healthy bone density, isn't elderly or frail, they're going to be much less injured than if someone in their 90s who has osteoporosis fell from the same height and landed in the exact same way.
People can occasionally survive hitting the ground after falling from high enough height to reach terminal velocity, e.g. falling from a plane without a parachute. Survive is very rare but possible
http://www.dailymail.co.uk/news/article-435377/The-man-fell-12-000-ft---survived.html
And people can die from falling on their head from just a couple of metres if their head hits something in such a way that it causes fatal bleeding on their brain. People have been killed with just one punch - either the punch itself causes a brain bleed, or their head hitting the ground or some other object on the ground causes a brain bleed. Having alcohol in your blood increases the risk of bleeding in the brain if you sustain a head injury.
So the height of the gantry makes little difference. It'll be well within the height range where both death and survival are plausible. Additionally, it's likely to have a wooden floor, which will have some give, and this will increase the chances of survival compared to a harder surface like concrete.
If you want your character to die from the fall, have them land on their head (especially if the side of the head strikes the ground first) or the side of their head hits a hard object as they land or on the way down. They suffer a subdural haemorrhage and die. With brain bleeding, you can also choose if the character has a period of being conscious before they die or not. Being unconscious after impact and never regaining consciousness before dying is very plausible, as is having a "lucid interval" where they are conscious - can even be fully conscious - before deteriorating, losing consciousness completely and then dying. You know that card you get in A&E in hospitals if you hit your head - the dial 999* if you get any of these signs/symptoms - those are the signs/symptoms of brain bleeding and your character would likely have some of those signs before they lose consciousness after the lucid interval. If you want them to have this kind of injury but survive, have a good team of paramedics arrive promptly and rush them to hospital (air ambulance if set in the UK as they have specialist teams with more resources for dealing with severe head injuries before the patient gets to hospital). They'll probably need brain surgery (ask doctors, especially air ambulance doctors, for the finer details).
*I presume they have the same thing in the USA but they would say dial 911
If you want your character to survive the fall, then they can land on a flat, wooden surface, not particularly awkwardly, but some other part of their body that's not the head takes the brunt of the impact. They'd likely suffer broken bones, but not a fatal head injury. Bear in mind that breaks to large bones such as the pelvis or femur can cause fatal internal bleeding, so if you want them to survive without medical intervention, don't have them break those bones. But if you want a big medical drama followed by a stay in hospital possibly including surgery, then do have them break those bones.
ETA: also, I don't think there'd be a standard height for something like this. Theatres vary a lot in size. So that gives you a lot of leeway.