怖い and 危ない: fear and danger
Separate a feeling of fear from dangerous conditions, recognizing that the same object can receive either judgment for different reasons.
Something that feels frightening
暗い道を一人で歩くのは怖いです。 says that walking alone on a dark road is frightening. 怖い, read こわい, focuses on the feeling of fear.
その話は怖かったですが、作り話でした。 says that the story was frightening but fictional. Fiction can feel 怖い without presenting an actual danger.
A dangerous action or condition
車道で遊ぶのは危ないです。 says that playing in the roadway is dangerous. 危ない, read あぶない, evaluates a situation that can lead to an accident or harm.
危ないから、そこから離れてください。 asks someone to move away because it is dangerous. It warns them to change their behavior rather than asking whether they feel afraid.
A lack of fear does not remove danger
本人は怖くないと言っていますが、その行動は危ないです。 says that the person reports no fear, yet the action is dangerous. Feeling and situational danger are separate judgments.
怖い先生 can mean a teacher who feels intimidating. Replacing it with 危ない先生 can suggest a dangerous person, so the two are not interchangeable.
Does 怖くない alone establish that a situation is safe?
Show the answer and why
No. It describes a lack of fear; whether there is actual danger is a separate question.