Is the belief that God sends signals to His servant through daily events or fleeting phrases—such as seeing the word "stop" as a warning, or hearing the phrase "put your trust in God" as an encouragement—correct and does it have a basis in Islam?

Coincidences have no bearing in Islamic law, and it is not permissible to rely on them to abandon a decision or to do something. Rather, a Muslim should perform Istikhara (prayer for guidance), seek counsel, study the aspects of the matter, and then act upon what seems best to him. So, after performing Salat al-Istikhara, the person seeking guidance should do what they deem appropriate, whether their heart feels at ease or not, for what they do will contain goodness and benefit for them. The hadith does not stipulate the condition of a feeling of ease, and abandoning a matter one has resolved to do because of pessimism is forbidden in Islamic law. Reliance on Allah (Tawakkul) is one of the greatest acts of worship, and its essence is to depend on Allah while taking the necessary means.