As you say, 이 밤이 싫어 means "I hate this night" but the two are structurally quite different.
"I hate this night" is structurally equivalent to "나는 이 밤을 싫어해".
싫어해(싫어하다) is a transitive verb like "hate", and 밤 is the object, 을 the object marker, and 이 (this) modifies 밤.
(이 before 밤 is just a pronoun "this" modifying the noun - it is non-essential)
싫어 (from 싫다, not the same as 싫어하다) is an intransitive, adjective-verb which doesn't take an object.
It is one of the "direct sentiment" adjective-verbs commonly used in Korean, which have no counterpart in English.
Structurally, 이 밤이 싫어 is similar to "This night is loathsome".
It has "night", the object of the sentiment, in the subject role, and has no verb or object but just an adjective
싫어 is like an adjective which means "arousing a resentment for it in me", and functions like a verb.
Another example: (나는) 네가 좋아 ((As for me) You are lovable) == (나는) 너를 좋아해 (I love you).
The two English phrases do not mean exactly the same thing, but the Korean ones do.
So you need to get familiar with these two types of phrases.
The first one (네가 좋아) is usually preferred, but it can only be used for the first person "I".
그 사람은 네가 좋아 or 너는 사과가 좋아 are bad sentences, for example, so you must use 너를 좋아해, 사과를 좋아해.
For the other example, we say 이 사과가 싫어 (이 after a syllable with 받침(bottom consonant), 가 otherwise).
You can also say 이 사과 싫어 without changing the meaning, but it doesn't sound as smooth in this case.
Also, when you are learning, it is a good idea to become familiar with the normal, full form including the particles.