Okay, so many things to talk about here,
1. The Rode NTG-2 is a MONO signal mic meaning you will only get sound from one channel – so that’s normal and perfectly fine. You actually don’t need stereo to record, for instance, interview audio and you can always create a sort of “fake” stereo using two mono tracks although purists will argue over that.
2. Why you are getting noise off the unused channel probably has to do with the cables and adapters
3. The most important thing to understand is that the audio circuitry in practically all DSLR cameras is ugghhhh….very very poor, put it that way. Probably what is happening is the automatic gain control (AGC) built into the audio circuitry is raising the levels of the signal coming from your mic so much that you are getting a ton of noise. Particularly if the camera is expecting a stereo signal coming in it’s going to try and raise the level of the track/channel that has no sound on it as well which is going to give you nothing but noise.
4. Can you do without an external recorder? There are some other options but think of them as less-bad solutions not great. For instance you can buy a special cable from a company called SESCOM (like their LN2MIC-ZMH4-MON Line Out to Camera Mic In Headphone Tap Cable) at https://www.bhphotovideo.com/c/buy/SEL2MZH4N25D/Ntt/SEL2MZH4N25D/N/0
ps: I have no affiliate marketing relationships with either Sescom, B&H or frankly anyone at this point
that is designed to take the signal from your mic and make it better suited for your camera’s audio circuitry while also providing you an extra connection to plug your headphones into so that you can actually monitor your audio while recording which is really a must have ability. I actually use this cable myself.
5. The other thing you might look into is to see if by any chance your camera’s menu options give you the ability to turn of AGC (Automatic Gain Control) or to reduce the gain on the camera’s built in audio.
I hope that helps you.
Steve Crow