Is it permissible to offer hospitality, such as tea and coffee, to a Christian neighbor who visits us on regular days and during Ramadan?

There is no harm in showing kindness to peaceful disbelievers, especially those who are neighbors. It is permissible to host a Christian female neighbor, but it is not permissible for a man to sit with her or to offer hospitality to her directly, because she is a non-mahram to him and may not be veiled. Rather, his wife or sister should handle that. Also, it is not permissible to offer her things that break the fast during the daytime in Ramadan.