Like Kid is any valid source of information on the Tesseract. Sure, the time she's been waiting may equate to 10,000 years in OUR world, but it's pretty obvious the Tesseract works on a different time frame (how it works is debateable) and I just don't think that Schala, no matter how noble, can keep sane for 10,000 years of existence. Come on.
I think time in the Tesseract is relative, like in Ender's Game series by Orson Scott Card. Traveling at light speed or faster makes time pass much slower than those outside the vessal, or in this case, the tesseract. I'm not sure what the ratio would be.
But lets assume that for each year spent in the Tesseract, the relative difference outside would be 1000 years. In that case, Schala might have spent at the most, 10 years there. This is most likey VERY wrong, though.
The idea behind the Tesseract is that it's empty 4 dimensional space. The term Tesseract describes the 4 dimensional equivalent of a cube. you can find pictures of it on google, and it's pretty brilliant.
If you view the Tesseract as a vessal that is capable of moving in the 4th dimension, you can assume that all time is within reach from within it, also because it has a 4th dimension itself, it is essentially limitless in size. Moving within the tesseract in our basic 3 dimensions would get you nowhere, the only way to enter and leave is via gates, which are 5th dimensional tunnels. 5th dimension being theorized to be a dimension of movement in which one can travel instantly to any location, like a kind of subspace. Imagine a rat in a maze, it moves in two dimensions, but if ti were capable of the third, it would simply rise out of the maze to reach the end. A nigh instataneous mode of transportation that avoids the normal obstavles of matter.
so, while the 3rd dimension allows one to move uninhibited by the obstacles of mass, the 5th dimension of movement would theoretically allow one to move freely of the other element that impedes all movement, energy.
Remember, this is just a theory.
Edit - Also, for mitosis to occur, the orginal doesn't have to be destroyed, it's simply reduced in size until it can re-form. Like I said, starfish. Cut off a starfish's leg, wait several weeks, and you'll now have two complete starfish, both genetically identical. With the huge amount of energy that lavos has been storing, I think it's possible that it uses it to reform its lost pieces after reproducing.