Question about Panasonic RF-2400DEG-K

Can be operated with 4 AA batteries

No idea, it is only used with a power cable, maybe ask the manufacturer if this is possible.

I only use it with a power cable. It has a battery compartment for 4 x AA batteries, but I can't tell you whether the radio will run smoothly with rechargeable batteries. According to Google, some devices are not designed for rechargeable batteries because they have a lower voltage. For this question, you will probably have to contact the manufacturer if it is not mentioned in the item description/technical data

I haven't tried it, but yes, why not?