What is the function of a salt-bridge in an electrochemical cell to actually migrate ions from one half-cell to another OR the salt-bridge sucks up the ions from a half-cell to make the half-cell neut?

Answer 1

The salt bridge exists to provide the electrical connection between the two reaction vessels while keeping the two reactions separate. The salt bridge provides a path for the charge carriers from one half of the cell to the other half. They migrate along this path when the circuit is closed, driven by the attraction of the anode for electrons or electron-rich species, and the attraction of the cathode for positively charged ions.