A lot of questions here, let's tackle these two first:
4.And last but not least, what's SpaceX's solution for the oxygen-rich environment at 377bar, 748K injector and 546bar, 811K pre-burner?
2.The Raptor's oxygen pump sits directly on top of the main combustion chamber, while the SSME's two pumps are on the opposite sides of the main combustion chamber. Why couldn't the SSME use a similar configuration with oxygen-pump pre-burner on top and HP oxygen impeller discharge directly on top of the main combustion chamber?
The space shuttle first flew in 1981. Back in the 1970's when it was being designed, the Americans weren't trying to build oxygen rich staged combustion engines as they assumed there was no alloy that could handle the conditions. This effectively precluded the Americans from developing staged combustion kerosene engines, as a fuel rich staged combustion kerosene engine would suffer from coking.
In the 1990's, after the fall of the Soviet Union, the Americans got their hands on some old NK33 engines and found that the Soviets had solved the materials problems of oxygen rich combustion in the 1960's! The Soviets had thus been able to use staged combustion on Kerosene, as in the RD170 from Soviet heavy launch vehicle Energiya (which carried Soviet shuttle Buran on its only spaceflight in 1988 before the collapse of the Soviet union caused the budget to disappear) and its derivative the RD180 (which was sold to the USA) (source: Wikipedia)
Following on from this Soviet / Russian experience, SpaceX has developed its own alloys, which are most likely very expensive and difficult to work with.
The oxygen pump therefore probably sits on top of the combustion chamber to keep the oxygen path as short as possible. This means Raptor is a very tall engine. It looks like the nozzle is less than half of the total length, whereas it is more than half in most other sea level engines. I'm not sure how SpaceX propose to mount the Raptor, but if they use top mount like the Space shuttle engine, that nozzle is going to swing a long way horizontally for just a few degrees of gimballing! A possible solution is to mount the engine inside a ring gimbal. I would guess the space shuttle main engine designers, who were working with a fuel rich cycle, decided to put the pumps beside combustion chamber to keep the engine short and ensure the engine didn't need too much space to swing.
Additionally, as noted in the Stanford SSME presentation linked below, the location of the turbopumps on the SSME made them easily replaceable. The oxygen turbopump was complex, having a helium purged seal between the fuel rich turbine and the oxygen pump, for safety reasons. The hydrogen turbopump was complex because it needed several stages to achieve a decent pressure while pumping the least dense liquid known.
Raptor's turbopump cannot be worked on without removing the engine from the vehicle. It is however specifically engineered for long term reliability. One of the reasons SpaceX chose full flow staged combustion was to simplify the turbopump seals, with each turbine running on a gas mixture that was compatible with the liquid being pumped.
3.Why Raptor opts to use the methane discharge fresh out of the fuel pump instead of the aft of the nozzle cooling circuit to use in the oxygen-rich pre-burner, as the latter is a supercritical fluid (methane goes supercritical at 45.99bar and 190.56K) and has better combustion than the former which is a true liquid?
This is probably to improve control and throttling. A true liquid has a defined density, and is therefore easier to meter than a supercritical fluid, whose density is pressure and temperature dependent.
- The Raptor doesn't have an LP fuel or oxygen pump...
I have to agree with Johneye that we cannot draw too many conclusions about how complex an engine is from a drawing, as it depends how much detail is shown. One thing we can see, however, is that the SSME has those LP pumps. I don't think the Raptor is particularly unusual in not having them. The RS68 (SSME's closest relative) has only single shaft turbopumps, see page 3 of http://www.rocket-propulsion.info/resources/articles/PropulsionForThe21stCentury-RS-68.pdf
Note that the Raptor probably does have multiple stages on a single shaft in order to get the required pressure. The drawing in the OP shows 2 stages on a single shaft in the Methane pump.
What makes the SSME different is that it uses separate, lower RPM booster pumps on separate shafts. The reason for this is to avoid cavitation, which occurs when fluid near its boiling point is agitated such that bubbles are formed and then collapse. An additional precaution is to use large bore pipework. It would seem that these low RPM pumps did not gimbal with the engine. Instead they were fixed and fed by large bore pipework. Discharge from them was then fed to a smaller bore articulating duct and from there to the main pumps, at sufficiently high pressure to avoid cavitation. See page 18 of this PDF from Stanford.
There are several reasons why Spacex might not need to use this solution:
- Not every other engine uses it (in fact there are few that do.)
- SpaceX likes to subcool propellant to increase density, but it also has the benefit of reducing cavitation.
- At least half the Raptors on Starship, and most of the engines on the Super Heavy Booster do not gimbal, so there is no problem with providing them with large diameter inlet piping. Maybe SpaceX does use low pressure pumps on those engines that do gimbal.
As a final note, it's a mystery to me why the SSME needed a low pressure pump for oxygen. The oxygen was stored at the top of the external tank, and would have been under several bar of hydrostatic pressure due to gravity/thrust at the inlet of the engine. On the other hand the hydrogen was stored at the bottom, so there would have been little hydrostatic pressure.