1. what os are you running and will it be online all the time?
(if not i have webhosting and you have an account, dork!

)
2. just forward port 80 to the ip of the computer that the webserver of your choice sits on.
3. notepad works, if not, use something crazy like dreamweaver
4. yes you'd have to code the php, there is no visual editor lol.
your decision to make a php website could be quite an undertaking or not one at all. go sit at a book store like b&n or borders and read up on the concepts of php first with a sheet of paper and a pen.
try some of the examples and use php.net a lot, all the info you'll need for php is there if you're willing to understand it.