So pretty much if a christian falls into sin they are damned to hell for all eternity?
That rather depends on what you mean by “falls into sin”. Also there is a variation on people’s theology here: some believe that you cannot lose your salvation, and some (myself included) believe that you can reject God after becoming a believer. Hebrews 6:4-6 says “For it is impossible for those who were once enlightened, and have tasted the heavenly gift, and have become partakers of the Holy Spirit, and have tasted the good word of God and the powers of the age to come, if they fall away, to renew them again to repentance, since they crucify again for themselves the Son of God, and put Him to an open shame.” So, based on the verse, if a person rejects God (and this is not just accidentally sinning, but willfully shaking the love of God and purposefully sinning), then there is no return. So, if by “falls into sin” you mean willfully rejecting God, then yes, if sinning accidentally, no. Those among us who believe that a person cannot lose their salvation don’t think this really makes a difference though, since they wouldn’t have fallen away in the first place. You are welcome to judge for yourself on that point.