Is being bothered by one's fiancée's reproach for sending messages of advice and supplication online justified, and should one refrain from messaging to avoid misunderstanding, especially given the agreement between both parties not to communicate by phone or online, and to suffice with weekly visits?

Advising has its etiquettes, among them a good approach and avoiding giving advice in front of others. Your annoyance with your fiancée's style of advising is natural. There is no harm in the suitor corresponding with his fiancée out of necessity, provided it adheres to শরীআ [Islamic law] guidelines. However, it is preferable to avoid this to block off any means [to sin] and to prevent problems before marriage. Caution must be exercised regarding leniency in family gatherings, and emphasis should be placed on the covering of women and lowering of the gaze.