Yes, saving faith is demonstrated through God working in us to will and to act according to His good purpose. The justification of a Christian which happens after Salvation (which happens by faith) involves our faith moving us to act out of love for God, helping to demonstrate that our faith is genuine.

Abraham's belief is when God called him His friend, and it was credited to him as righteousness, and Abraham's actions proved that his faith was genuine.

Works do not save. We want to do good because we are saved, but all our righteousness is as special as a used tampon in God's eyes. Only through faith in Jesus and His work are we saved, and only through Jesus are our works acceptable to God