3point is correct. The Eagle Lunar was tiny. It wasn't designed to do much more than take two astronauts to the moon and little else.
Correct, this is not just a repeat of Apollo. The Apollo missions had to fit everything within a single Saturn V launch, so the lander was absolutely minimal. Not so this next time.
For the HLS to work there will need to be multiple propositioned fueling craft. I believe the idea is these spacecraft will have to be orbiting the moon and the HLS will rendezvous and fuel up for descent and ascent.
In either competitor's scenario, the lander will be fueled in Earth orbit. SpaceX HLS needs the lander and at least one tanker, although probably several. The lander is launched dry into LEO where it will be fueled by a series of subsequent tanker launches. Then when full, it flies independently to the Moon and enters lunar orbit. The crew launches in Orion using SLS, flies separately to the Moon, and rendezvouses with the lander in lunar orbit. After landing and then returning to lunar orbit, the lander is discarded to a graveyard orbit and the crew returns home in Orion.
The Blue Moon lander will use the Northrop Grumman Cygnus spacecraft as its LEO tanker and a booster stage being built by Lockheed Martin as its translunar stage. Otherwise the mission profile is essentially identical. Both competitors will need to solve the problem of orbital propellant transfer, which no one has ever done before.
But I assume people have done the math.
The math isn't actually that hard in the mission planning stage. The remaining delta-v capacity of a spaceship is proportional the specific impulse of the fuel and the natural logarithm of the mass ratio—the Tsiolkovsky ideal rocket equation. The mass ratio is the wet mass divided by dry mass. As propellant is expended, the mass ratio changes and therefore the remaining delta-v changes until MR = 1 and ln(MR) = 0. Starship's MR is reported to be about 26. For comparison, the Saturn V mass ratio is 23.1. Obviously in a multistage system you need to carefully consider each stage separately.
What you can't do as easily with simple math is determine whether a crew can operate the ship, land it, and get into and out of the ship when it's on the lunar surface. Apollo conducted extensive studies of this on the ground. A total of 12 LTAs (Lunar Test Articles) were built. As a result, after LM-1 did its uncrewed test flight, the ship configuration did not change materially through the remaining crewed flight tests: LM-3, LM-4, and LM-5. LM-2 was built as the twin for LM-1 and is now in the National Air and Space Museum as its test flight was canceled. Even when the J-type lunar modules were flown starting with LM-10, the configuration did not materially change beyond being heavier and putting the rover in a planned-for but previously unused equipment bay. Because of the extensive forward-looking ground-based work, they did not have to requalify the ship for flight.
