1. I use DreamWeaver ... nice, but it has some rough edges as a mac program, feels like a windows port in a lot of places. Also, it's really not free.
2. You need to set up DNS so that the name you bought points to the IP address you have. This assumes you have a real, and static IP address. If your IP address begines with 10. or 172. or 192. or if it changes all the time ... you're screwed. You need to pay me $20 / month to host your site for you.
3. anything after the / is the path on the computer, and is resolved by your machine. Before the / (between http slashes and the slash after .com) are the internet resolution and that's where DNS comes in. The root of the site on your machine is at /Library/WebServer/Documents - put your files there to show up at your.ip/
if the first thing after the slash is a ~ then your machine (and the apache webserver) interpret this to be a request for a user's directory instead of the web root mentioned above.
On the subject of DNS, I'll give you some specifics in hopes of squashing any ambiguity in my explanation. If you registered with Register.com - you'll be able to log in there and specify the IP of the machine you'd like the name to point to. This will magically make yourname.com/ come up the same as your.ip/
If you registered with Network Solutions, you'll need to provide a DNS server ... a brief explanation...
When you type in a name of a place on the internet you'd like to go, your request first asks the master servers on the internet who holds the information for this domain? The answer points to your DNS server. Then, your machine has to ask the DNS server what machine is pointed to by this specific address. The answer is your.ip. Then the client proceedss to make requests from your.ip
Register.com provides DNS servers for you that you can modify so that all you have to provide is a machine running a webserver (or whatever) whereas Network Solutions only provides master lookup so that you can specify your DNS server. If you don't have your own DNS server ... $20 ;-)