v1-10 - Remember the context of these letters we've been reading to Pastor Timothy and Pastor Titus. These men did not have the benefit of being able to attend seminary or have access to hundreds of inspirational books and videos published every year on how to do this or that in the church, so Paul wrote them these letters to give them a crash course.
Chapter two makes clear a big part of the job: teach.
Teach the older men (v2), older women (v3), the young men (v7) and even the slaves (v9) (remember, most people were slaves in that day & age).
Pastor Titus will be able to do this because he himself has been taught by grace to say no to the world and instead live a godly life (v11-12).
You may not be a pastor or elder, but this same principle applies to you as well. As you are taught by grace, you have a responsibility to be teaching all those you are in relationship with.
v11 - The NIV translates v11 as "the grace of God has appeared that offers salvation to all people." Most of the other translations state that God's grace has appeared bringing salvation to all people. Doesn't this seem like proof that salvation is universal, that is, all people are saved rather than just a certain few? Is the NIV translation leading people to a false theological conclusion?
It is certainly true that God's grace brings salvation to all people (that's literally what the Greek text says), but this doesn't mean that all people are saved by it.
Just like the old saying says, 'you can lead a horse to water, but you can't make it drink.'
All people have grace offered (brought) to them,
but only those who have been graciously regenerated (born again) by the Holy Spirit will accept the grace that's been brought to them.
It's hard to arrive at this conclusion simply based on this one verse, but one of the key rules of biblical interpretation is that scripture interprets scripture.