Is it permissible to invite a Christian friend to eat from the Aqiqah or from an animal slaughtered for the sake of Allah, and can she be given a share from the Udhiyah (sacrifice)?

There is no harm in inviting a Christian woman to partake of the 'aqiqah (definition) meal, especially if her conversion to Islam is hoped for, or if she is in need, in accordance with 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." However, if her conversion is not hoped for and she is not in need, it is preferable not to invite her and to prioritize needy Muslims and relatives, due to the Prophet's (peace be upon him) saying: "Do not accompany anyone but a believer, and let no one eat your food except a pious person," and his saying: "Charity given to a poor person is charity, but when given to a relative, it is two: charity and strengthening ties." The prohibition against associating with the impious refers to close interaction that could corrupt one's faith, not to depriving them of kindness.