Is it permissible for me to send messages to a girl I admire concerning religious or general topics that do not stir emotions or instincts, or is that forbidden, and must I cut off all communication with her and suffice with supplicating for her to be my wife?

If you are currently unable to marry, there is no need to think about marriage or speak with the girl. When you are able to (materially and physically capable of marriage), then you can inform the girl of your desire to marry her. It is impermissible to speak with her or message her without need, as this could lead to forbidden matters or the girl becoming attached to you without you being able to marry. Therefore, it is advisable to cut off this relationship and strive to attain the ability to marry.