HM-10 BLE Module - not working

HM-05 page? Do you mean HC-05 (http://www.espruino.com/Bluetooth)

I don't have a HM-10 here to test with, but as far as I know (in answer to your questions)

1. The power should come from the same place as in the HC-05 (the 2 corner pins near where pin A4. Most of the pads are not connected to anything, so it won't actually matter if you solder them - as long as they are not shorted together.

2. Yes, even if you connect only the two power pins, I believe you should be able to pair it, so my guess is that somehow power is not connected up.

3. That won't be an issue when writing Serial1.print("AT")/etc. What it's saying is that the 'console' - the thing you're writing commands into - will be on USB... But when you power from a wall supply it'll automatically move to Serial1, so you can program Espruino over bluetooth.

Having said that, HM-10 is different because it's BLE, so I don't believe it'll directly emulate a serial port.

1. He's connecting to the pin holes on the prototype area as a way to connect up the resistor/switch - which is why there seems to be a blob. The connection with the resistor and switch is so you can put short the pin to ground with the switch, but it will normally be at 3.3v. For now it might be worth forgetting the switch and just connecting the pin to 3.3v with a resistor.
   
   

Pin 24 is optional, but as it's a status LED, it might help you find out what's going on.

1. First port of call would be checking that the module has power - maybe look at the datasheet and find some gnd and 3.3v pins, and then check with a volt meter.
   
   

Next I'd probably try and put the status LED on so you can see the state of the module.