I wanna ask is there anyway to have customized WordPress image URLs? For example, http://www.mywebsite.com/wp-content/uploads/2011/01/mypic1.jpg change to http://images.mywebsite.com/great-image/mypic1.jpg
You are talking about creating a sub-domain just for your images, which is good in terms of loading the images a little fast. But, when it comes to SEO advantage, there is no difference between the two as search engines index the name of the image file. So it does not matter whether the image is on the same wordpress installation or being loaded from a sub-domain.
yes it is possible. first make a folder name "great-image" the go to settings -->Media. At the end of media options page, there is a option "Store uploads in this folder" with empty field. Insert the URL where you want to store your images. like URL would be "http://images.mywebsite.com/great-image/......"
I am not really sure that will work for a sub-domain that resides on another server than the WordPress install. The way I read the documentation is that if you leave the default upload filepath blank (defaults to 'wp-content/uploads'), you can specify an URL to point at that upload path. This is kind of like a permalink is handled. There is no need to create a folder for it either. I might be wrong on this part though, but sub-domains I am pretty sure you cannot do without having FTP access.
you either have to run a sync script to keep you images updated on you host with WordPress installed and the host with the subdomain settings, in this case i recommend you a cdn, and WP-super cache in the cdn settings you can set it up to pint to a url for imges, css and javascripts. also you have to make a cname for the "subdomain"