"I am afraid of storm" doesn't speak correctly to me as a native English speaker. "I am afraid of storms," "I am afraid of the storm," or even the oddly phrased "I am afraid of a storm" would be correct. (Though I'd only use the last example as part of a sentence; "I am afraid of a storm passing through my town.")
No, it can't ;)
Well... maaaaybe in some rather colloquial language, because we have a lot of weird (from the point of view of a non-Polish person) constructions with Dative, which work like 'something happened to me', for example "Zupa mi się wylała" is like "The soups spilled... to me"? So I can maybe imagine "Pies mi się boi fajerwerków", which would mean that my dog is afraid of fireworks and it affects me because I have to care for him. I can maybe imagine it, not sure if anyone would actually say that.
Anyway, in your sentence, the storm is afraid (of... we don't know what).