Bindoy, I am not quite familiar with the UB1204 mixer but it seems it has a pre fader switch. With that, I think the better way of doing your recording, if you do not want the vocals recorded to tape is, - mic to input 1 of mixer. Connect DVD to Tape output of your mixer, which is in parallel to the main output of the mixer and is -10. Connect your CD player into inputs 5/6 or any inputs 2 to 8. Open up the aux send pot of the mic. Do the same with the CD which plays the backing tracks. Press pre-fader switch of the CD so that you can monitor the backing tracks without putting up the faders of the CD input, otherwise the backing tracks will be recorded together with the voice. Press also the pre-fader switch of the vocal input. Balance the sound going into the DVD recorder by making the choir sing using channel fader and seeing to it that your VU meters hit just a little over or under 0 Vu. Connect your headphone amp into the output of aux send 1. Balance backing tracks and vox so that the singers can hear both in a very nice fashion, using the aux send1 master for the proper volume level. Hit record! To monitor what you have recorded, connect the output of DVD to the tape input of the mixer.
Your noise problems, I believe come from multiple connections as well as mismatched impedances - -10 and +4 connections, plus your long cable lines. Also,too much routing or connections can also cause latency problems.
Make your routing simple. Shorter cables and less connections make recordings clearer and fuller.
Am I making sense? Correct me if I'm wrong. FWIW