Is it possible to design the business objects based upon an XML schema and populate them based upon an XML file?

P.S. The data would come in a format defined by an external system, not a dataset in XML format.

Yes.  Look at the sample that comes with the framework titled "XML Data Source through Business Object."  One thing that you can do to produce the strong-typed properties is create a Faux table in the DDT and then map to that DDT table ( you will never deploy the DDT table is it is just for mapping).  Then use the CopyDataFrom method to load the BO.

Can you also generate the business object from an XSD or do you have to use a table?

To generate the schema for the business object, you have to create a table within the Database Deployment Toolkit and build the business object from it.  You don't have to deploy that table to a SQL Server or anything, it just has to be there to map to it for the BOMapper structure reference.