"I assume the benefit to your launcher is overcoming the initial inertia (does inertia change when a mass is accelerated?) of the rocket as well as the advantage of an equatorial launch location. "

No, I wouldn't describe it that way. A large rocket requires tons of fuel to get the rocket to the same speed as could be gotten by a pipelauncher. As far as inertia, you could say the pipelauncher would have same inertia as the rocket, thereby it would be *similar* to a stage separation- as compared to the typical launchpad of having a fire pit and flowing in tons water so that rocket exhaust is cooled as rocket slowly accelerates off the pad.
The main benefit of a pipelauncher is that it should lower the cost of launching rockets and increase the amount of payload a rocket can deliver to space.

"At 100 psi (How many CFM do you figure?) what rate would you is able to displace the water and at what rate would the rocket/launcher be accelerating after 200 meters."

The key to how a pipelauncher works depends it's bouyancy in water. If you had a pipelauncher which was say 800' long/tall it should float vertically about 200' above the water with a rocket on top of it. If you were to go inside the pipelauncher, the air pressure would be about twice normal around 30 psi & the water level inside the pipelauncher would about 30' below sea level. If you were to add more air or increase the air temperature inside, the pipelauncher it would rise. If you were to let air out or lower the air temperature, it lowers. The air pressure would remain fairly constant regardless of how high it's floating- this pressure is directly related to the of water level inside the pipelauncher compared to outside (the ocean) water level. Increasing the pressure above 30 psi will give you acceleration. One way to get an idea of the energy/power involved is to think about dams. Dams are powered by the height of the water they are holding back- which is atm per 33 feet of height. The problem with thinking about dams is you might think a pipelauncher is powered the water jetting out the bottom- this is only a minor factor. Letting water in and out is just a convenient way of controlling the force of the pipelauncher's buoyancy (think of ships being able to "lift" huge amounts of weight).
[Note:The pipelauncher could remain vertically stable at 200' above the sea level, but during a launch sequence, it would start at sea level and continue to accelerate above the 200' level]

The speed of pipelauncher's acceleration of a rocket would probably be limited limited to sub-sonic speeds. But you would probably limit the first pipelaunchers to speeds of around 200 mph- roughly meaning designing pipelaucher about 800 ft tall and having it accelerate at less than 1 gee. It's possible to make much larger pipelaunchers and/or pipelaunchers that can accelerate faster than 1 gee (but the present rockets probably couldn't easily take this much acceleration).

"What is the source of the compress air (gas?)? Is the air pre-compressed in a storage tank(s)?"

Yes. The pipelaucher is constructed from pipes and these could hold compressed air, though the source of power would mainly come from heating the air and thereby increasing the air's volume.

"Are these questions in-line or did I misinterpret what you presented?"

Better than most:)