So I was wondering how come liquid rocket engines (operating in the lower atmosphere (such as launch stages)) are using Oxygen that they have packed on board. What I mean to say is why would the rocket need to waste space and mass bringing Oxygen with them in the launch stage when they could use air intakes to fuel engines with Oxygen? I do not understand why really big liquid rockets (like the Saturn V) could not fuel their lower stage engines with Oxygen from the atmosphere instead of using packed Oxygen. I guess my reasoning is that using Oxygen already on the rocket at launch is heavier than packing just liquid fuel (keep in mind this applies only to low atmospheric stages because there is an abundance of Oxygen) and taking Oxygen from the atmosphere as needed along the way. Anyway, clearly I am missing something here, or else all launch stages would be using intakes right? There must be some reason why this is not feasible.
So here's my questions:
1) Why don't launch stage liquid rocket engines use air intakes to supply Oxygen instead of Oxygen tanks so that they weigh less and can carry a larger payload?
2) Can rockets like the one pictured above even work?
3) Would air intakes on the side of the rocket be useful so that payloads can be placed on top?