Yes, this works according to the manufacturer's instructions.

I haven't found out yet, but it's the same for us. What I have noticed is that the batteries are empty again in no time. I have already tried x different batteries, always new ones, and after only a few hours they are empty again. Does anyone else know this problem?

The supplied!?

This is an error on our side. All other colours in this model range also have Bluetooth.

Yes it has. :) From page 20 in the manual you will find the information: - https://static.digitecgalaxus.ch/Files/9/0/5/9/6/3/6/web-retro-mini-manual-DE.pdf

You can connect your MP3 player via the AUX-In connection on the back. So headphone connection on your MP3 player to the AUX-In connection. For example, with the following product: Roline Stereo jack connection cable (2m, Entry, Black) Enclosed are the instructions: https://static.digitecgalaxus.ch/Files/9/0/6/6/8/2/4/web-retro-mini-manual-DE.pdf

It is best to contact the customer service department directly regarding price questions. See also: https://www.digitec.ch/de/Wiki/4490