1. First off I would suggest familiarizing yourself with the differences between wordpress.COM blogs, and self-hosted wordpress blogs.
User advertising is, except for a couple very narrow exceptions, not allowed on wordpress.COM. For the exceptions, see the last sentence under "Affiliate marketing blogs" in the bottom set of bullet points in the "types of blogs" link below.
Since you have your own domain name, you can get the domain mapping upgrade and have your blog here show up under that domain name.
2. Typically moving over here is very simple. You export from your existing blog (tools > export) and then import into the new blog here. During the import here, you can choose to have wordpress.COM import all of your images and documents (.doc, etc.).
3. We cannot add themes at wordpress.COM. We are limited to the themes found in the dashboard under appearance > themes. Themes found on the internet are for self-hosted wordpress blogs using the software from wordpress.ORG.
We cannot edit the underlying theem PHP script files here at wordpress.COM because this is a multi-user platform which means we all share the same underlying theme and wordpress files. Any change by one person would change it for everyone using that theme.
If you have CSS editing experience, you can get the CSS upgrade, which will allow you to stylize the themes here, but it does not allow you to change the functionality. CSS is also themes specific so you cannot use the CSS from one theme with another theme. Before buying the upgrade, you can go to appearance > edit CSS and wordpress has provided a preview function where you can try out changes before you buy the upgrade.
4. No, no bandwidth or traffic limits. There are blogs here that get hundreds of thousands of hits each day.