What is the ruling on adding non-Mahram women or accepting their friend requests on Facebook with the intention of spreading good and inviting to Islam, while observing the Sharia guidelines, and is this considered corruption and unlawful mixing?

If the internet is used to spread good, such as for Da‘wah (inviting to Islam) and education, it becomes a great blessing. For whoever calls to guidance will have a reward like the rewards of those who follow him. As for merely accepting a friendship request on the internet, it is not considered unlawful mixing, but it must be for a Da‘wah or educational purpose, while adhering to the Sharia (definition)-compliant guidelines, such as not publishing anything inappropriate or that incites discord, and avoiding private messages and chats with women, as this is a great door to Fitnah (temptation/strife).