it is normal that the unregulated voltage is much higher without load.
Is your BS the correct base for that HS or did you changed it?
In other words, did both worked already together?
There are two MK1 versions, one is not multibase able. There is a software update for the HS produced prior 2006.
did you purchased thm from different sellers?
If so, the dont work together unless you update the firmware to a newer multibase version.
And yes you can connect to the base even it is not connected to the line.
2 lines for germany is correct.
Did you tried a reset of your HS and then try to connect to the base again?
Base must be disconnected from mains for a while then it is in connect mode.
PS: Is it a real base or only a charger. Can you provide a photo of the base and powersupply?