"It is dark in the evening."
くらく is the dictionary form of the verb for "dark". くるい is the adjective form of "dark".
When you state that something is NOT something, you use the dictionary form + 〜ない. (Note: this makes it an adjective.) But this is a casual use. To make it polite, use です after it.
くるい is the positive adjective form of "dark". くるくない is the negative adjective form meaning "not dark".
To state that something IS something, use the adjective form.
今日はくるい。It is dark today (but this is impolite).
To make it polite, use です.
今日はくるいです。It is dark today (polite way).
To make it negative, use the ない form. 今日はくるくない。
To make it polite use です. 今日はくるくないです。
I think using the term 'casual' would be more fitting than "impolite". It's not really impolite to say くらい after all, but it may be a bit too casual depending on social context.
Both are used to describe temperatures.
涼しい (すずしい) is "cool."
寒い (さむい) is "cold," but only in relation to the weather. If a thing is cold to the touch, you'd use 冷たい (つめたい) instead.
寒く is the adverb form of cold. It also means dull/weak so i guess "weakly" would be the most likely place to see it.
You use "kuraku" if the sentence is negative.
Kuraku nai desu.
It's not dark.
You do not modify "kurai" in affirmative, present tense sentences.
Did we learn dark before? It only provided the kanji, when all the answers were in hiragana...