I'm wondering about what Christianity (and The Bible) says about a) sex education being thought in schools, and b) people learning about music and playing music instruments. Is it ethical to learn these two? Or is there any barrier or limit to learn them?
The Bible would say nothing about sex education being taught in the schools because that was, and still should be, the responsibility of the parents. The reason we may need sex education in the schools in America is because parents have been clearly unwilling to teach their children, themselves. At the time of the writing of the New Testament there were few of what we would consider schools. There were, of course, Torah classes for Jewish boys. The Greek philosophers had their own disciples that they taught their philosophy. But there were few schools that taught a broad variety of subjects, like modern schools. Therefore, the Bible is silent about what should or should not be taught in such schools.
The only passage that would seem to prohibit learning and playing music is Amos 6:5. I will quote the entire context, though, because many people who use this passage ignore the context.
"Woe to them that are at ease in Zion, and trust in the mountain of Samaria, which are named chief of the nations, to whom the house of Israel came! Pass ye unto Calneh, and see; and from thence go ye to Hamath the great: then go down to Gath of the Philistines: be they better than these kingdoms? or their border greater than your border? Ye that put far away the evil day, and cause the seat of violence to come near; That lie upon beds of ivory, and stretch themselves upon their couches, and eat the lambs out of the flock, and the calves out of the midst of the stall; That chant to the sound of the viol, and invent to themselves instruments of music, like David; That drink wine in bowls, and anoint themselves with the chief ointments: but they are not grieved for the affliction of Joseph. Therefore now shall they go captive with the first that go captive, and the banquet of them that stretched themselves shall be removed." (Amos 6:1-7)
Clearly the prophet is not condemning music itself, but those who let their leisure time pursuits take precedence over their concern for the spiritual welfare of the nation. He is condemning an attitude of "why should I worry?"
Obviously there is no prohibition against studying music because music has been a part of worship to God for centuries. The book of Psalms is a songbook for use in the Temple worship.
Are there limits to what one learns in these areas? I think so. In the case of sex education in the schools I think the parents of each child should determine whether they participate in the classes. Since most such classes don't teach values as much as Christian or Jewish parents might like, the parent has to decide how much they will teach and how much they will allow the school to teach their child. In the case of music I think the passage in Amos quoted above sets the limits on study. When one's pursuits take priority over one's study of God's word, then the limit has been reached. As long as one does not allow his studies to take him away from God, then there is probably no limit. Again, though, the Bible is pretty much silent on this as well, other than to say that we should put God first (Matthew 6:33).