Why not?! You will not be able to define Entities as SEAM components, or use built-in components like EntityQuery, but everything else should work.
Moreover, if you search the Javadocs (and perhaps the source too), you will probably find that SEAM has extension points for different persistence architectures. As an example, EntityQuery extends Query extends PersistenceController<T>. You may be able to extend PersistenceController<T> with your own implementation. NOTE: This is only speculation, I haven't implemented it.
Yes, of course (it is not as easy at it should be, because the default configuration is to use JPA, but where I work we have many projects with Seam that do not use JPA)
Please vote for JBIDE-2630, it will make it possible to create a Seam project without JPA project easily.