Gravity head was negligible. In fact, with the LM in an upright orientation, the engine injector was about level with the top of the propellant tanks, thus there would be essentially no gravity flow to the engine. Propellant flow was provided entirely by pressurized helium.
Now that I think about it a bit more, I think the system probably worked better on the Moon. Since most of the propellant was positioned below the elevation of the injector, it had to be lifted up to the engine. This requires less work in the low gravity of the Moon (or under the low acceleration of the LM in flight above the Moon).
What were the advatages of using helium tanks, was it another case of reducing the number of moving parts to save weight and reduce failure risks?
A pressure fed system is obviously a simpler and more reliable system. With no turbines or pumps there are few fewer moving parts to fail. However, a pressure fed system can weigh more than a pump fed system. In a pumped system only the pumps and downstream piping must be rated for high pressure. The tanks themselves are pressurized to fairly lower pressure, perhaps only a couple atmospheres. However, when there are no pumps to boost the pressure, the entire system must be pressurized to a pressure high enough to push the propellant out of the tanks, through the piping, and into the combustion chamber. The tanks must withstand a pressure of perhaps 10 to 20 atmospheres, which means a thicker wall and more weight. There is also the weight of the pressurization system. I imagine there must be a break even point were the increased weight of the propellant/pressurization system is exactly balanced by weight savings realized by the elimination of the turbopump machinery. I don't know on which side of that break even point the LM's system fell.
As far as the use of helium, versus some other gas, is concerned, I can think of a couple reasons. First, helium is inert and won't react with either the fuel or oxidizer. Second, it is lightweight. For example, in comparison to nitrogen (a likely alternative gas), helium has only 1/7th the mass at a given temperature and pressure. There are likely other reasons for using helium that I haven't thought of.
