Is it permissible to eat food offered by a colleague who does not wash her hands after eating pork, and how can this colleague, who is far from religion and knows its rulings but does not apply them, be guided?

You must advise your colleague to obey Allah's commands and avoid disobeying Him, and warn her of the danger of her state if she dies before repenting. If she is guided, that will be counted among your good deeds, for the Prophet, peace and blessings be upon him, said: "By Allah, for Allah to guide one man through you is better for you than red camels." If advice does not benefit, then abandon her as a disciplinary measure. If you despair of her reform, then it is obligatory to leave her company and cut ties with her, for associating with her may bring harm. The Prophet, peace and blessings be upon him, said: "The example of a good companion and a bad companion is like that of the musk seller and the blacksmith's bellows." If your colleague gives you food after peeling it, there is no objection to eating it unless you know that her hand touched something forbidden or impure, for food is not to be discarded based on doubt.