First, not all sins are the same (See 1 John 5:16-17).
Second, sometimes Christians need to mature before they can walk uprightly with the Lord. It is not always an overnight process for some believers. They need to study and learn the Word of God. That takes time. That does not mean they have a license to sin, though.
Three, Christians should obey the posted speed limits. While I believe it is a sin to go over the speed limit a little (like say 5mph), I do not believe it is a grievous sin that leads to spiritual death (i.e. the Lake of Fire). Yes, I am aware of Romans 13. But what is the context? Is it talking about minor infractions of the Law? I do not believe it is because Romans 13:4-5 says that if you do evil, be afraid, for the higher powers (government authorities) are a minister of God who does not bear the sword in vain; They are a revenger to execute wrath upon that person who does evil. This sounds like major transgression of Law to me here because they tell the reader to be afraid whereby they will throw you into prison or execute you for committing a major crime. However, if the police or judicial system does not punish you for going over a little (like say 5mph), why would God condemn you? But if you could be thrown in jail for going over a little, then I think it would be a big deal to break this kind of Law because the law is considered to be a serious infraction for that government. Also, if we are driving in such a way that puts others at risk by us going excessively fast, that is a serious lack of love of your neighbor and I would consider that a grievous sin. All God's laws are based upon loving God and loving your neighbor. If we have gone over the speed limit in a way that is too fast, we should repent and ask God for forgiveness, especially if the Lord convicts us of this sin. So while it is important to take seriously all the laws of the land that do not conflict with God's laws, I do not think minor infractions is what is in view of Romans 13 (even though we should obey the traffic laws as best as we possibly can). Remember, Jesus desired the Pharisees to focus on doing the weightier matters of the Law like love, justice, faith, and mercy (Which they did not obey - See Luke 11:42, and Matthew 23:23).
Unintentional sins is not not the same thing as willful sin. If you were not paying attention, you could easily do this. This does not mean you committed a grievous sin. If you intended to run the light, then that is not good because it would not be loving your neighbor in the fact that you could have caused an accident. But if your mind was elsewhere and you were not intending to hurt anyone, then that is different. Also, Romans 13 is in view of major infractions whereby you can go to prison and or be executed. For it says for you to be afraid, for the higher powers do not bear the sword in vain.
With the help of the Lord Jesus Christ, we can control our thoughts believe it or not. Bad thoughts in most cases are a salvation issue whereby we need to confess such sins immediately and forsake them. For Jesus said that looking upon a woman in lust it can potentially cause a person's entire body to be cast into hellfire (See Matthew 5:28-30).
Romans 13:14 says put ye on the Lord Jesus Christ and fulfill not the lusts of the flesh. Galatians 5:24 says they that are Christ's have crucified the affections and lusts.
This is a salvation issue if we do not repent of such a thing. Jesus says a person defiles themselves not by what goes inside them but what comes out of their mouths. Jesus says your words can condemn you (See Matthew 12:37). So it is important to guard our words in what we say and make sure they always uplift God and His good ways.
I think it depends on what you mean here. If a person doubts God's salvation later down the road, than I would say that is a very serious problem and it is probably the result of grievous sin in one's life that they did not repent of. Hebrews 3 warns not to let sin deceive you for it can cause a person to have an evil heart of unbelief whereby they can depart from the living God. Departing from God is not the same as backsliding into sin while believing in Jesus. Departing from God is denying God's salvation or denying God's existence after a person was once enlightened by the Spirit. Such a thing is apostasy and it cannot be repented of.
Again, not all sins are the same (See 1 John 5:16-17).