What is the difference between tiyarah (ill omen) and fa'l (good omen), and what is the meaning of tatayyur (taking an ill omen)? And is the accidental occurrence of words similar to what I am thinking about a warning from Allah or a form of tiyarah?

Good omens (fal) and bad omens (tiyarah): Both involve the soul attaching itself to what it hears or sees, be it speech or an animal. If it perceives good, it is from having a good opinion of Allah. The opposite is tiyarah, which is taking a bad omen from something disliked or evil. There is nothing in Sharia called "warning messages from Allah." Thinking about something feared, then hearing words that allude to it, is a form of tiyarah. Its cure is reliance on Allah and believing that He alone brings benefit and averts harm. Tiyarah is a form of shirk because people believe it brings benefit or averts harm. The meaning of dispelling it through reliance on Allah is to entrust all affairs to Him and not act upon such thoughts that arise.