戦争に なる おそれがある literally means "There is the likelihood of a war breaking out" and does not mean "I worry there might be a war." I also added an example.
Q: can this be used with adjectives, or just verb-plain?
この車は高いおそれがある I worry that this car is expensive. 〜高すぎるおそれがある ~ too expensive
Is this always used for things that have a negative outcome?
Yes, おそれ is related to "fear" so that the expression generally relate to those that have a negative consequence.
この車は高いおそれがある is awkward and not normally used. 〜高すぎるおそれがある is okay but still somewhat awkward. 恐らくこの車は高すぎる may be acceptable..
I ran these examples past a native speaker (a teacher of English). From what he said, if it refers to something physically happening (a war starting, a house collapsing, etc) then おそれがある is natural. If it refers to a situation (as in 3294) then だろう is natural sounding.
I should add that he said that all the examples were gramatically acceptable - only that some didn't sound entirely natural.
恐れ おそれ (n) fear/ horror/ (P) (WWWJDIC) Q: is the kanji ever used in this contruction?
懼れ or 虞
#7181 - Is this sentence correct? It sounds more like is should say: There is no fear of this illness being contagious.