Regarding Free Will, The DHARMA Initiative and the current state of The Others
The Lost Experience suggests that The DHARMA Initiative failed. This may have been the horror of horrors for the original team; if the equation factors cannot be changed, then this may be evidence that Free Will may not exist.
Plan B for The DHARMA Initiative became, "If we can't change destiny, can we survive the inevitable instead?"
And that is what the Others are now - a cradle for humanity after everything else fails on Earth. An ideal, well supplied, mini-society that serves as a failsafe.
Evidence of The Others' good health and physical strength suggests that they may be been chosen for their physical qualities - they are Good People.
Arrival of the Losties represents an opportunity and a danger - the Losties may be good additions to their group. Or they may contaminate it.
Not all The Others believe in this Plan B and hold out hope that free will DOES exist but may admit that it might be very rare. Finding individuals that may possess the capability of free will is an ongoing effort. Immediate scrutiny of the Losties arrival may be evidence of the intention of finding candidates.
The reason for Skinner Box experiments on the Losties may be an effort to discover people who can make decisions uninfluenced by environment, which may be evidence of Free Will.
The founding of the original DHARMA Initiative was intended to be a multi-discipline effort. To have conflicting ongoing research initiatives to find a solution - any solution - would not be incompatible with the original mission of the initiative.