Your SAC rate is variable. It can go from .4-.5 for a calm relaxed diver to over 3.0 for a diver in distress or panic. It's usually expressed as an average, compiled over time. We use different rates for calculating different things.
Just for an example:
Resting/deco/ SAC might be .3-.4
Relaxed experienced diver on an easy dive may be .5
A working, nervous, inexperienced diver may have a .75
An excited or panicky diver might have a SAC in excess of 1.5
Your SAC rate may not change, but since it is calculated at the surface, the volume of gas as it relates to a given SAC will increase as depth increases. You will use gas 4x faster at 100' than you do at the surface. At 200' it's 7x faster. {(Depth / 33) + 1 gives you the factor}
Regulators are designed to deliver air at ~135 psi over ambient pressure. So providing there is sufficient pressure in the tank, the air delivery from the regulator will be sufficient to allow your lungs to inflate as you breathe.
However, gas is denser at depth (one of the reasons for using helium on deep dives) and this, along with the increased pressure on your body will contribute to an increased work of breathing (WOB). This can lead to additional problems, such as a build up of CO2, which is bad anytime, but especially at extreme depths where the effects can be amplified.
Equipment, training and understanding has allowed tech divers to routinely push depths of 200-300' that used to be considered extreme. I know of some people that have conducted dives in the 300-400' range on a fairly regular basis. There are even some that I know of that are pushing stuff in the 500-600' range from time to time.
These are people with thousands of hours of experience on SCUBA, dealing with problems and knowing how their body reacts under such extreme conditions. Once you leave the recreational range of 130' and start to cross into the technical depths things change. You no longer have the option of making a direct ascent to the surface if you have a problem and your thinking has to shift to allow you to solve problems,
any problems at depth.
Failure to do so often has dire consequences. For an example of that, read this recent thread:
http://www.scubaboard.com/forums/accidents-incidents/343188-two-divers-die-wazee-lake-wi.html