A true Christian is a regenerated one. By being obedient to the Word ( The 3rd chapter of John and Romans 10: 5-15) we, the born-again, have gone from hearers to believers to followers to doers of the Word of GOD because His Holy Spirit lives within us. It is HE that has been given to us, by faith, and helps us to grow in grace as a new creation as beloved children of the Father of Lights. b) Yes, Christians are still prone to making mistakes because we are STILL in the flesh even though our spirit has been regenerated. Just like a baby makes mistakes, by trial and error, while navigatin through this world - it is the same for the Christian. We are learning to fight our own fleshly desires as we yield more to the unctionings of the Holy Spirit. It's a daily war ( Galatians 5:17 and James 4:1 and 1st Peter 2:11) between our flesh and spirit as to which will take control. We are "unlearning" old ways as we embrace our "new creation"selves as we learn to live in alignment to GOD'S WORD. c) As to problems with faith: yes and no. The problems only come when you doubt the things that Jesus said and did. As long as you REALLY believe that Jesus is who He said He is, and believe EVERYTHING THAT HE SAID AND DID, then losing your faith is not possible. Why? Because of the indwelling Teacher : the Holy Spirit. He guides those born-again into ALL truth (John 16:5-15) I've been IN CHRIST over 40 years, and I STILL am in awe at how HE opens up new truths in passages of Scripture that I have read many times before. d) Do we fall? And, if we do, does that mean that we no longer believe. Let me encourage you to read what the Scripture says about the "how and why"people "fall away" by examining the Parable of the Sower (Matthew 13:3 - 9 /18 thru 23 or Luke 8:5 thru 15). Those of us that had the Word - Seed take root are yielding the "fruits of the Holy Spirit" ( Galations 5: 22 - 25). As we allow the Holy Spirit to have His way and grow spiritual fruit in us...as we hear continue to hear the voice of our Great Shepherd ( John 10: 27-28) ....it becomes impossible for us to become nonbelievers. When you look at both Peter and Judas, disciples that were with Jesus Christ from the beginning of His earthly ministry, you can see the contrast of what it looks like to yield to fleshly temptations even though you knew the Lord...personally. And, their outcomes were so different, weren't they? If you have anymore such questions - I recommend the desirringgod.org website. Pastor John Piper's teachings on being regenerated are second to none. Blessings!