This is a great ship

Yes. I did not bother with such parameters at the time. Sure it can ruin somewhat your immersion. Also, the spacecraft is a ramscoop. It somewhat saves fuel tank mass

Saturn V is also fully loaded with cryogenic fuel (emphasis on fully loaded). There's very little empty space inside compared to what such spaceship would have.
The mass could still be a bit better estimated, but it's not that bad.

But in the end, Space Engine only ever uses ship mass to calculate the ship's acceleration if you update it in the ship editor. It is not used for anything else, other than aerodynamics, which this ship doesn't have anyway.

The mass of this spacecraft is reported to be 900 tons. The mass of the Saturn V according to Wiki is reported to be 2970 Tons (I presume fully fueled&loaded) and its length ~ 1/4 of the La Neige. What kind of material is it supposed to consist off so that it can be so light?

I took this long for someone to say this

Can't seem to get docking to work. There's options for various ports but the green docking guids appear hundreds of meters behind the ship when I choose them.