If you're Twitter account isn't protected then anyone can follow you unless you block them.
If your Twitter account is not "protected" then anyone can view your profile.
Sometimes, it depends how well your twitter account is protected and how many people search you. ;)
You can tweet someone even if their account is protected.
Even though the account is protected, you can still mention people normally by writing their username (@username) in your tweet.
Any Twitter user can send you a tweet if your account/tweets aren't protected.
Yes they see it.
You can look at anyone's Twitter account without having an account. Simply type the URL in the address bar of your browser. However, if their account is protected/private then you won't be able to view it.
If the account is not protected then you can view it without anyone knowing.
If you included their full username (@username) then that tweet will appear in their @replies even if your account is protected.
If your account isn't protected then everything you tweet is searchable.
Yes they will become public.
If your tweets are protected then only people following you can see your tweets. If she isn't following you then maybe she has access to an account that is following you.