Yes, sims do age normally in Granite Falls. There is no restriction on vacation, you can go as many times as you want and you can go as long as you want.
As for mentoring, you can do it to your spouse or children. Have them play the violin or guitar, then your music sim should have the option to mentor them. It is hard to mentor NPC, as it is hard to catch NPC sim playing violin or guitar. With sims in your household you can control, much easier.