Yes genuine faith results in repentance and obedience, fruit and good works are the result.
Well, yes, the Holy Spirit will propel a believer to be faithful to Him. The question though is how much after salvation works are you going to tie to salvation itself? If it is 100 percent Jesus saving you and not yourself.. then the measure of the salvation surely isn't the works they are doing after conversion.. but whether they purely and simply believed on the Lord Jesus Christ.