On the island and alternate dimensions:
The law of conservation of mass, also known as the principle of mass/matter conservation, states that the mass of a closed system (in the sense of a completely isolated system) will remain constant over time. This principal is equivalent to the conservation of energy, in the sense when energy or mass is enclosed in a system and none is allowed in or out, its quantity cannot otherwise change (hence, its quantity is "conserved"). The mass of an isolated system cannot be changed as a result of processes acting inside the system. The law implies that mass cannot be created or destroyed, although it may be rearranged in space and changed into different types of particles; and that for any chemical process in a closed system, the mass of the reactants must equal the mass of the products.
Fred has worked this out to mean one of two things when it comes to the island:
a) She's been transported to an alternate dimension, just as she was transported to Pylea. This means that all other people and structures that have appeared at random on the island have also appeared from other dimensions. Life does not go on without people back home. Any claims to this effect actually refer to alternate dimensions where Fred was never transported to Tabula Rasa. Dimensions are not, in fact, created by Tabula Rasa itself, in accordance with the many worlds interpretation.
b) Somehow the island has managed to create an alternate her. Every person on the island was somehow brought into being by the island itself, and they're no more than copies. Time and life goes on back home as if they'd never left, because they actually haven't.
While theory A is the most plausible, Fred had to let herself believe B for a while in order to not drive herself crazy wanting to get home. She's aware that A is likely how things are, and as such, is still looking for a way home, even if she'll admit that this dimension isn't to bad, as far as alternate dimensions go.
Links for Reference:
*Physics and String Theory for Dummies