Student or Learner
It must have happened a long time ago.
--- Is it OK to use the present perfect and AGO in such a sentence?
Because I thought it's not quite OK to use the present perfect and AGO in the same sentence.
I've seen her a long time ago OR I saw her a long time ago.
You're right. "I have seen her a long time ago" is not correct.
The phrase "It must have happened" is about the only use I can think of where you can use this form. Might have, should have, could have -- all subjunctive mood type phrases. Unless you are using this kind of expression, you must use past perfect.
I knew her a long time ago or I wish I had known her a long time ago.
I have known her a long time ago. No, no, no. no.