i swear to God if they tried to answer the light / heart of the island and the word Midichlorians was brought up i would've destroyed my TV hahaha
i think that people could only find the island if Jacob allowed it and since so many of the names in the cave of candidates were Dharma people that could be a reason why they found it so easily.
i don't know
i liked the fact that they didn't answer everything because you can use your imagination to come up with something you're satisfied with personally. it's sometimes nice to have things be a mystery open to interpretation.
i would also assume that since Kelvin and Radzinsky were still in the hatch pushing the button that the Dharma Initiative would still leave the food drops. plus the D.I. might not have even known about the purge since the others probably didn't do the purge and then gloat to the D.I. about it.
plus with Ben, Ethan and possibly other Others being D.I. people it was probably quite easy to lie to the mainland D.I. people and continue to get the food drops, etc.