Is it permissible to give charity to a non-Muslim, and is its reward equivalent to the reward of giving charity to a Muslim?

There is no objection to giving voluntary charity to a non-believer, provided that it is not used for anything prohibited. The one who gives the charity will be rewarded for it. As for obligatory charity (Zakat), it is not permissible to give it to them. It is recommended for the one who gives charity to prioritize the needy, and that which strengthens and exalts the religion.