I have been reading various chapters in the Bible over the last few days and they all seemed to be connected to faith being what is needed to be saved and to give the hope of eternal life (I love how the Lord connects these things!!)
When it says that faith in Christ is all that is needed - what about sin? If we do not repent, or do not make efforts to change, do we still have the hope of eternal life? Is it necessary to repent?
I know that in my relationship with the Lord, I want to do right by Him and change to become more Christlike, but if someone has faith, but does not repent and continues sinning with no intention to change/ stop... does this make much difference in the end?
Lets not forget that we are saved by grace THROUGH faith, not saved by faith, although I trust that this is what has been meant by many here who have added 'what is meant by or how do we define faith'. Faith working through love is how we can accept the gift of grace in our lives...but even the best of our faith, with the best of our efforts, with the best of our love will still fall short of the glory of God and we will still 'require' His grace.
We should exercise caution when seeking 'all that is needed', as in seeking 'just enough' or 'with only this one thing' and come to a deeper understanding of what faith really calls us to be. You are on the right path when you say above that in your relationship with The Lord that you want to do right by Him and change to become more Christlike; this is the call to all believers.
In looking at some of your other questions: 'Is it necessary to repent'? Yes. Repentance makes up part of faith. So I think it could be argued that the hypothetical person in the next question does not actually exist: the person who claims to have faith but does not repent and has no apparent intent to change, is precisely the type of person pointed out by Jesus in Luke 6:46, 'Why do you call me Lord, Lord, and not do what I command'? So while this hypothetical person might verbally say that they have faith...they have a house that is built on sinking sand as the song goes...
So Jesus teaches that obedience is also part of faith.
He also teaches that forgiveness is part of faith.
Loving God and loving others is part of faith.
Our sufferings, and 'enduring' through them is part of faith...St. Paul tells us that these sufferings and enduring them (which can be said to mean not giving up in our faith) are what unites us to Christ.
Our baptism joins us to Christ too: we share in His death and Resurrection, and thus baptism is part of faith.
The Eucharist (Lord's Supper if you prefer) is also part of our faith: Scripture reveals that in 1 Cor. 10:16: 'Is not the cup of blessings which we bless a sharing in the blood of Christ? Is not the bread we break a sharing in the body of Christ?' It is through faith that we can believe St. Paul's words to be true.
Faith thus has many moving parts...some, we as individuals, 'get' better than other parts. And even when we get it 'right', we must be humble enough to still know that we need His grace. Our faith is in Him and His promises, and not in our own feeble selves. Which is why, in judgement, God looks heavily upon our intent, and not necessarily at our 'outcomes'...there are many parables that demonstrate this: the parable of the widow who gave two pennies comes to mind...outcomes are nice and can be useful, but the intent of the heart matters more to God.
As to the last part of your question: 'does it make much difference in the end'? God is both merciful AND just: He offers His grace to everyone; but not everyone accepts His grace through faith. It is also important to keep in mind that it not for us to judge, and your hypothetical person could have a 'death-bed' conversion and would recieve eternal life from God through His grace...the same gift a person who lived their faith every moment of their life would (parable of the laborers). For while we will fail to live up to our end of the Covenant, God is always true to His end, and He never ceases in calling us to Him. Our faith, which can include all that I mentioned above, is the answer of our heart to His call.
Helpful?
Peace in Christ
Hawkiz