Is dealing with bank loans forbidden, and if so, why do some scholars permit it out of necessity, by analogy with carrion? And does this analogy apply to adultery, drinking alcohol, and theft in cases of extreme necessity?

Every loan that stipulates an increase is usury (riba), forbidden by scholarly consensus. If some scholars permit this loan due to necessity, there is no issue, for "necessities permit the forbidden," like drinking wine when facing death from thirst, or stealing food for someone on the verge of death from starvation. As for fornication (zina), there is no necessity for it, and it is not permissible to commit it, even if coerced, according to the majority of scholars. Some scholars, however, have permitted it under specific conditions.