Teenage is a stage in a person's life where discovery of oneself is being built. Teenagers usually wants total freedom and would try all things new to them. If in case they commit mistakes on their way they may learn from it. My answer is yes and no. As long as their likes are safe then they should be free. If in case the situation is detrimental to themselves and others then it should be regulated.

Yes, they'll learn much from different experiences - so they should be allowed to make some bad one (they're very educative) too. Nevertheless, it mainly depend on their age and their maturity, so parents naturally decide very carefully whether let their children do something or not, and which experiences they can be allowed to make. Never forget parents always care and worry about their children, as if they were still babies; this may annoy you but definitely it's parental love.