But, with this Arduino code, if you use the Serial Bluetooth Terminal app, and you send 1 or 0 what do you read on the Serial monitor (or still nothing) ?
I’d rather have used “false”…..
Please take also a look here:
in my post #6 I’ve added an interesting link to a HC09 that behaves like your “fake/weird” HC05. It seems that there are rubbish commands that seem to be irrelevant for a proper working, while on the contrary they are necessary (don’t ask me why 
).
Last,but not least, be sure to use the latest BLE extension. In the same thread there is the link.