Hi!
1. The pins CTS/RTS on the module are shorted.
why? just let them float . . .
Well... I shortened them in a desperate action

according to google, that means you've sent an improper command while in command mode . . .
uhm... I don't thing this is the real problem cause the commands are introduced right (95% sure), I explain:
When you are in "command mode" you have some ways to connect to the remote address using for example some of the next commands:
ACTION COMMANDS
C - Connect immediate to stored remote address.
C,<address> - Connect to address.
CF<address> - Connect Fast mode to address.
CFR - Connect Fast mode to stored remote address.
CT<address>,<timer> - Connect, required address, optional disconnect timer in ΒΌ seconds.
F,1 - Enter Fast data mode, end configuration immediate.
so for example if I introduce: C,<mac_address_of_my_usb_dongle>
I receive this "ERR-connected" message...
In other hand, when I want just to connect in "data mode" to the module, the connection established then the red LED turns off, but no green LED is activated and the data transmission does not work...
I think is broken...