ssh is the best!
not sure about icecast
I would try apache first, it is the only one I know but at least it is robust.
Yes, if you do get it up and running you can see it from the internet using your ip address.
Yes, if you get a domain you will get a www.something
address as well.
I use no-ip
but it's just for fun!
samba is quick and easy to setup. doit!