How does the researching to get to the mirror world work exactly? Does it increase by your squad's collective research points every interval of time?

You select a squad, hit the left most button to begin THAT squad's research, come back in a day when they have found their way to the mirror, then it behaves like any other battefield interaction on the normal world- except when you lose/get kicked off, you have to research your way back AGAIN. Every squad must research individually. 

Research per time interval is the sum of all of your (squad) pets' research potentials combined. Pets earn research potential by completing tasks which you can view by hovering the ? next to research potential and clicking "details." So some squads will be much faster or slower than others.