4.On what basis had the Galatians received the Holy Spirit?

On the basis of receiving by faith the Lord Jesus Christ, who had been revealed openly before them.

The saints in Galatia had received the Holy Spirit by believing in the atoning death and triumphant resurrection of the Lord Jesus, not by being circumcised and obeying parts of the Law of Moses. Therefore they are to obey the Gospel of Christ and not be concerned with the Law of Moses.