What is the ruling on seeking help from a Christian to find employment, and is it permissible to show him affection, inquire about him and his health, and greet him with peace?

It is permissible for a Muslim to seek assistance from a non-Muslim who is peaceful towards Muslims in worldly matters such as medicine, agriculture, industry, and employment, as the Messenger of Allah, peace be upon him, did with Abdullah ibn Urayqit. It is also permissible to accept a gift from a non-Muslim and to give a gift to them, based on the Almighty’s saying: (Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly).

This does not fall under the prohibition of al-muwalat (taking non-Muslims as allies or protectors), for the prohibited al-muwalat is aligning with non-Muslims against Muslims, or being pleased with their disbelief, or imitating them and loving them.

Some scholars permitted greeting a non-Muslim for a need or for companionship, such as Sufyan ibn Uyaynah and Abraham, peace be upon him. This is indicated by the hadith (definition) of Usama ibn Zayd that the Prophet, peace be upon him, "passed by a gathering in which there were Muslims, Jews, and polytheists, and he greeted them," and the hadith of Abdullah ibn Mas'ud who greeted a non-Muslim for companionship.

As for inquiring about the well-being of a non-Muslim, there is no harm in it, and the proof for this is that the Prophet, peace be upon him, visited a sick Jewish boy.