I've often wondered why carry O2 when the atmosphere has so much of it? I assumed it had to do with the required complexity of the engine so it could operate at different speeds and at different levels in the atmosphere. Is this just a "concept", or has an engine of this type ever been tried?

Why does the outside air have to be pre-cooled before being used as an oxidizer? And is there a potential problem with the N2 in the atmosphere causing corrosion in the engine, or create a toxic nitric acid exhaust (HNO3) or condensing prematurely (it evaporates at a different temperature than the oxygen).

What is the density of liquid hydrogen? I once heard 0.1 g/cm**3? How can you carry enough of it if it's that light? And what is this I hear about carrying the H2 in a semi-frozen slush? You should be able to carry more in a given volume that way.