I'm at a total loss to understand some of the basic concepts.

If I tweet something does everybody who follows me see it?
If I direct a tweet at somebody specific @piet does everybody who follows me see it?
Does all Piets followers see it or does me have to re-tweet?
How do people know that two people are having a twitter war - can they only recognize it if they are following both parties, but aren't tweets directed at one another private?
How do you know what is trending in different regions?
Lets say my daughter is tweeting and receiving tweets for example and I am following her, would I only be able to see tweets that are not directed anybody specific or directly to me?
Do I see anything that comes to her or is that private?
How do 5 people participate in a conversation, do you have to direct vie @each of the 5 people in each message?