Hans,
Haupt- und Hilfs- Lenzpumpe = Main and auxillary (discharge) pumps. Lenzen means to discharge outboards. For tanslation purps I would call them bilge pumps. Lenz means spring time. Your translation program was thrown for a loop by the nautical verb 'lenzen' and the non-nautical 'spring'. Reason why the are not called bilgepumps on a sub, they are also functioning to pump out diving tanks etc.
Regler refers to Regelzelle = smallish P&S tank close to the boat's tipping centre, where filling and pumping out has no effect on the boat's fore and aft trim.
Free surface are indeed same as previously discussed.
Main pump much higher capacity than auxilliary one, thus might have had tendency to suck air in sloshing bilge and loose it's suction. This would not be a problem with the relatively short length but deep Regelzelle and it's shorter pipe distance to the pump manifold. Ofc filling a Regelzelle from within the boat, will not drive the boat deeper. Rgds, RB