Channel noise A and B channels AND headphones had noise in R channel

Most headphones (wireless) have a tuning wheel that allows you to find your headphone channel pair to base set. It sounds that while checking your foam ear piece you may have moved this dial / wheel. After locating (probably near volume) the control for tune, place headphones on and slowly move control for tuning. You should hear something move control to strongest signal.
your base also has settings switch for channel helpful if you have more then one pair in house, on different TV. Play with both to find best volume.

Sorry I have not had that problem with batteries but have had other noises and I usually stop using the headphones for a while and hang them up and start again.

It is a definite pickup grounding issue causing hum/"buzz" which diminishes when touching strings. Check the impedance of cable jack inputs and cable which should be 1/4"mono input/output jacks) . A personal preference but effective is to NOT run guitar direct into mixer but through an external amp w/ a headphone out jack . Noise gating/preamp filter also will help eliminate the "buzz"/noise from pickups. It is unfortunately the nature of the "electro-magnetic" beast when it comes to electric guitar pickups .Hope this helps.

Sometimes empty/unplugged channels introduce noise to the amplifier. You can always try to connect all of the input channels to some external mobile phone/mp3 player, etc. and then set these equipments to the minimum possible volume (mute if possible). This should remove the "atmospheric" audio noise.

That sounds like a bad connection but it can also indicate your mixer has a problem. If it occurs on all channels it is the mixer, if only one then the problem is in the input. Check your cables, they are a big culprut in problems like this.

Check that the noise is NOT a funtion of an "effect" that the MAIN runs through. Do you hear it via the main amps or is it just in the headphones from the main? Pressing a PFL for a channel should bring ONLY that channel into the headphones UNLESS other PFL's are down... and NOT affect the main. Something is not clear here.

It's because the TV's audio is stereo and the dialogue is mono split between two channels. When dialogue hits your headphones the majority of the mono signal gets cancelled. Try a different set of headphones or watch true stereo channels... IE movie channels

When you put your headphones in does it switch off the speakers? If it does it could be a faulty headphone jack.

yellow and red-green are most likely grounds. red is normally the right channel and green is normally the left channel. quick question though, why on earth would you cut the plug off of a pair of 75-90$ headphones?

Generally, crackling noises come from anyplace there is a mechancial connection for the sound signal. The volume control, main/remote speaker switch and possibly the headphone jack. That is where the contacts must be cleaned, but it requires dissassembly. Try operating the main/remote speaker switches, and plug/unplug a headphone several times. I am assuming there is still audio behind that crackling. Are you using both main and remote speakers simultaneously?