Thanks for the reference! You forgot to mention your work on drums enhancement, which may also be of interest for Summer_More_More_Tea's application. Well, that all really depends on what you want to do with it. Do you have a specific "end application" in mind?
I completely agree with pichenettes's above statements. To be complete, I should however say that the vocal enhancement you mentioned has also been used in some works by Matti Ryynänen, on Karaoke track generation, to enhance the results.
To answer your questions:
Given the effectiveness, which one is preferred(or any other solutions:)?
As pichenettes said, neither seems to suit your need: low-pass/high-pass filtering is bound to fail because of the harmonic structure of the human voice (and more generally of any "interesting" sound - i.e. anything beyond sinusoids...).
If the 2nd one, let two channels A and B, will (B-A) or (A-B) used when compute the background? As with merging two channels, does the arithmetic mean accurate enough?
Again, the second method you mention won't do because you can only remove the signal which is in the center, not retrieve it. In other words, even the vocals are in the "center", there is no simple maths to get a vocals only signal.
Or I can downsample each channel by a factor of two and interleave the downsampled signals as mono result?
er... averaging the channels to obtain a mono-channel signal, as suggested above, makes sense, and won't break the spectral characteristics of your signal (assuming the stereo signal is not degenerated). So you obtain a mono signal in which you have, basically, the same musical content as before.
Correctly downsampling each channel means you first apply a low-pass filter (with cut-off frequency of sampling_rate/4 in your case), and then you can safely take every 2 samples. There not much to say however about interleaving the channels thus downsampled: in most general cases, this is breaking the spectral characteristics of your signal. You probably do not want that.
Indeed, the operation of low-pass filtering followed by setting to 0 every 2 samples, and keeping these 0's leads, in the Fourier domain, to "mirroring" the low frequency components that were kept onto the high frequency ones. Remember you signal processing lessons on sampling theory: multiplying by a sequence of impulses (or diracs) results in a convolution with another sequence of diracs in the Fourier domain, i.e., in that case, the frequency spectrum of the signal is repeated (periodized) along the frequency axis, with a period equal to the sampling rate.
Normally, when downsampling, you remove the 0's (because you assume a new sampling rate). But here, keeping them results in very annoying additional high frequency components. Interleaving these signals is not going to correct this.
Well, all in all, the short answer: don't do that. :-)
At last, I might also suggest you to use the GUI I developed for the LVAICA 2012 conference: there is a git repo for it. I am still debugging and improving it, so comments are welcome :D
Hope that helps!