Is it permissible to eat meat not slaughtered according to Islamic rites and fish fried in oil in which pork is fried, given the unavailability of other alternatives in Japan, and is this considered a matter of necessity?

It is forbidden to eat pork or meat that has not been slaughtered according to the Islamic method. It is also not permissible to eat what has been slaughtered by idolaters or atheists.

If permissible food is cooked with oil that was used to cook pork or carrion, then it is not permissible to eat it.

You are not compelled to eat unlawful food as long as lawful food is available. Rather, you should agree with the hotel or another restaurant to slaughter and cook the meat separately from the unlawful, or undertake the slaughter yourselves if possible. Otherwise, be patient with eating lawful food such as fish and vegetables, for every body nourished by unlawful means, the Fire is more befitting for it.