Yes, you can use SharePoint Designer (SPD) to modify sites and content in Microsoft Online Services's SharePoint Online environment, as well as add data view web parts, etc. From the perspective of someone using SPD, there's really not much difference in what you can do in SharePoint Online as opposed to an on-premise SharePoint environment.
One thing you have to remember with the Shared version of SharePoint Online is that you can't deploy any compiled code to it, such as .MSIs or .WSPs (SharePoint deployment packages).
You can create site templates (.STPs) and deploy them to your environment by saving them into the Site Template gallery of each of your top-level site collections, then create new webs (sub-sites) using those templates. But, you won't be able to create a new site collection using that custom site template, you can only create web (sites) beneath your site collections with them.
You should be able to modify the files in your SharePoint Online sites with SPD and upload them back just like you would with an on-premise SharePoint environment.
There's also a full MSDN forum devoted to SharePoint Online you may want to check it out for more info on the platform:
http://social.technet.microsoft.com/Forums/en-US/onlineservicessharepoint/threads I hope that helps, let us know if this doesn't answer your questions,
John
MCTS: WSS v3, MOSS 2007, and SCOM 2007
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