A dedicated or unique IP address allows you to use an SSL certificate/secure hosting (https) for your domain, I believe it also allows you to have anonymous FTP configured. A unique IP also allows you to access your site by IP address, which is sometimes useful during DNS propagation etc.
There may also be advantages when it comes to search engine optimization, as you will not have to worry about any 'nasty' sites sharing the same public IP address as your site and possibly affecting its rankings.
DreamHost has multiple high speed pipes to the Internet. As for the speed you can expect from your particular server, this will vary greatly depending on the server you are on, who you are sharing it with and other things such as the time of day etc, so it is very difficult to give a concrete figure. I can say that I have seen in excess of 2MByte/s from my server when using WGET to transfer to a remote host.
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