Is it possible to connect microphone and charge the cam at the same time?
Here's how to make the external mic work while to have power to the camera.
You'll need to be able to solder small things and not be afraid to cut up the camera cables that you just bought, also a right angle micro usb housing or any plug housing that you want to use, small pliers or tweezers and a razor blade and a hot glue gun.
I have made extras if you just want to buy one just send me a message or email.
Cut the end off of your your power and mic cables
Cut all the way down with the razor just behind the indentions on the plug top
then slice down each side
score along the hard plastic all the way around and make score marks around the end too.
then slowly peel all of the rubber from the plug overmold off and you'll be left with this
Here is your pinout for the micro usb 8 pin plug, if your soldering kung fu isn't strong, find someone who has the right tools and skills otherwise you'll probably melt the plug or cross the pins.
test your connections and then fill the plug housing with hot glue when you close it to protect it. It should look something like this when you're done, I also added a female and male mic jack to disconnect when I don't use it.
Note: when you hook up the external mic it doesn't disable the internal microphone, it just adds to it.