Is it permissible to work in a restaurant that serves pork (as a dishwasher) temporarily until another job is found? And is it permissible to work in a women's salon for non-Muslims that uses wigs, artificial hair, cutting, and extensions?

It is not permissible to work in restaurants that serve alcohol or pork, nor in beauty salons that practice hair extensions (وصل الشعر) and eyebrow plucking (النمص), even if the work involves washing dishes or is for non-Muslim women, because doing so constitutes assisting in something forbidden. One should seek permissible work.