I'm concerned that purgatory does not exist in the Bible. I believe that imaginary doctrine can be changed, as has the belief of Limbo, with innocent newborn babies, who have died prior to baptism, no longer going to Limbo. I always thought that God has told us to believe in Him and we will be saved by His grace. "For it is by grace you have been saved, through faith--and this not from yourselves, it is the gift of God -- not by works, so that no one can boast" (Ephesians 2:8-9).
Maybe I've simplified this too much. Have I?
What you have stated is correct, but it can be misunderstood. Some people define belief as a simple affirmation that God exists and that Jesus, His Son, came to earth. James addresses this problem of belief being in word only:
"What does it profit, my brethren, if someone says he has faith but does not have works? Can faith save him? If a brother or sister is naked and destitute of daily food, and one of you says to them, "Depart in peace, be warmed and filled," but you do not give them the things which are needed for the body, what does it profit? Thus also faith by itself, if it does not have works, is dead. But someone will say, "You have faith, and I have works." Show me your faith without your works, and I will show you my faith by my works. You believe that there is one God. You do well. Even the demons believe--and tremble! But do you want to know, O foolish man, that faith without works is dead? Was not Abraham our father justified by works when he offered Isaac his son on the altar? Do you see that faith was working together with his works, and by works faith was made perfect? And the Scripture was fulfilled which says, "Abraham believed God, and it was accounted to him for righteousness." And he was called the friend of God. You see then that a man is justified by works, and not by faith only. Likewise, was not Rahab the harlot also justified by works when she received the messengers and sent them out another way? For as the body without the spirit is dead, so faith without works is dead also" (James 2:14-26).
Real faith is one that spurs a person to obey the things God has said. The passage you quoted actually says that if you read one more verse. "For we are His workmanship, created in Christ Jesus for good works, which God prepared beforehand that we should walk in them" (Ephesians 2:10). Man-made works cannot save a person, but God has prepared works for us to do which will impact our salvation. Thus we find Paul discussing, "Through Him we have received grace and apostleship for obedience to the faith among all nations for His name" (Romans 1:5). Paul ended the same letter stating, "Now to Him who is able to establish you according to my gospel and the preaching of Jesus Christ, according to the revelation of the mystery kept secret since the world began but now has been made manifest, and by the prophetic Scriptures has been made known to all nations, according to the commandment of the everlasting God, for obedience to the faith -- to God, alone wise, be glory through Jesus Christ forever. Amen" (Romans 16:25-27).
Belief in God is believing what God has told us, accepting it without modification, and making application of it throughout our lives. "But without faith it is impossible to please Him, for he who comes to God must believe that He is, and that He is a rewarder of those who diligently seek Him" (Hebrews 11:6).