late

  1. She married late(adv)
  2. She got married late(adv).
  3. She had a late(adj) marriage.
    Are all grammatically OK?
    Do they have the same meaning?

Yes and yes.

Mister Micawber,
“I haven’t been to the theater much late.”
Is this sentence OK?
If it is wrong, please correct and explain with grammatical reason.

No; an adverb is required:

I haven’t been to the theater much lately.

Mister Micawber,
When ‘late’ is considered both as adjective and adverb, we can use either ‘late’ or ‘lately’.
Why we must use ‘lately’ here?

‘Late’ as an adverb does not mean ‘recently’, as in your sentence. Check its meanings HERE.

  1. “I haven’t been to the theater much recently.”
  2. “I haven’t been to the theater recently.”
    Can I say as above?

Yes, those are fine.