We also wondered whether the remote control deserved the name. Even after changing the batteries several times, the problem persists.

Hello - the unit does not have a 12V connection. The battery has 14.4V - at best, the unit can be powered from a car battery via this connection - the battery is cleanly connected with a plug connection.

Yes, it is possible to use a non-stop function where the whole CD is repeated. You can hear the change from one track to the next for a few miliseconds. Otherwise there should be no gap.