Is it permissible to get to know a Christian girl for a month – without touching or transgressions – before officially proposing to her?

Conversing with a foreign woman is not permissible except out of necessity and to the extent of that necessity, as it is a great gateway to temptation. If the woman is chaste and marriage to her is possible without falling into a Sharia-forbidden act, then that is permissible. Otherwise, seek a righteous Muslim woman who will assist you in your religious affairs. Know that marriage to a woman of the People of the Book is permissible, provided she is chaste, but it is fraught with risks.