Is it permissible to extend the mourning period beyond three days due to the long distance and some people being late to learn of the deceased's passing?

There is no specific time limit for offering condolences. So, if the one offering condolences receives the news days later, there is no harm in offering condolences then. As for limiting the days to three, this applies specifically to a woman's mourning for the deceased, with the exception of her husband. The Prophet, peace and blessings be upon him, said: "A woman should not mourn for a deceased person for more than three days, except for her husband." Similarly, there is no known limit for neighbors and relatives preparing food for the family of the deceased.