Learn English – What does “be it” mean in this sentence

It means

I've almost but not quite given up dating ...

The All but part suggests the speaker has done everything.

But the expression is used when the speaker can't think of anything further to do, so it might not be literally everything.

night is young is an old idiom, Google Ngram has occurrences back to 1804. It means that it's early in the evening, although it's often used facetiously when it's getting late, but the speaker doesn't want to end the evening's activities. Wiktionary defines it as:

It's not very late (at night) and there's plenty of time.

faded is more recent slang meaning high on marijuana.

So the sentence you quoted is saying that it's not too late to get stoned.