Depends. Based on the IP in the email you may be able to identify where they live within a block. If they send the email from work
you may be able to identify the company name from the IP in the header
( even if they are using hotmail or yahoo ).
Always be at you best behaviour online. Normally, identifying who you are would probably require police assistance, but don't rule out the possibility that there are unscrupulous employees at some ISPs
who will sell you out.
Yes. I believe Fred is correct. However, I do not believe this would occur unless a party were to commit a serious transgression while online. Also, before police become involved in tracing someone, I believe a court order would have to be issued to allow pertinent information to be obtained from the ISP. (as far as I'm aware, anyhow).