Is it permissible to congratulate Christian female employees in a government department on their holidays, and is it permissible to return their greeting when they say "Good morning"?

It is not permissible to congratulate disbelievers on their holidays. If disbelievers greet with the Islamic salutation, they should be answered with "wa 'alaykum" (and upon you). If they explicitly utter the full salutation clearly, it is permissible to respond with "wa 'alaykum as-salam" (and upon you be peace). However, if they greet with something other than the Islamic salutation (such as "good morning"), it is permissible to return the greeting in kind, and many scholars have permitted initiating such greetings with them. As for returning the salutation to young, unveiled women, it is preferable to dislike responding to their greetings for fear of temptation. One should avoid mixing with women, especially unveiled disbelieving women, to safeguard one's religion and block the means to evil.