1. Let's not rush it.
(What does 'it' refer to? What other expressions can we use it instead of the sentence?)
2. Don't give up on your dreams.
3. Don't give up your dreams.
(Are both grammatical?)
In this sentence, 'it' is a reference to whatever is happening. It's quite vague when taken out of context!
Let's not rush things.
Let's not rush the situation.
Etc.
2 and 3 are fine, yes.