Are there any limitations to grappling?

I have tried searching in other articles about my question, but I have not found a definitive answer to my question.

  • If a level 5 barbarian equipped with a 2 – handed weapon attempts the grapple and achieves it, does the additional attack feature allow an attack with the 2 – handed weapon?
  • The next round of the barbarian arrives, can he still make 2 attacks to the weapon without breaking the grappling hook?

The rules for grappling stipulate that whoever initiates the grappling needs at least one free hand, so it was confusing for me …