1) By pages, what do you mean? Pages rendered in the PDF and manipulated in Acrobat, or body pages switched around within Designer?
2) you can use Global Data binding to populate evey Name field with the same data (assuming 'Name' is the same on every page)
3) Yes. You can use the signature field to lock a set of fields indentified in a field collection, and associate that collection of fields with the signature, so that after signing all fields in the collection become locked. This is the easiest way to achieve that. If you don't use signatures, you can write some script to change a certain set of fields to have an access property set to either "readOnly", or "protected". If the fields are readOnly, users can still tab through them, and copy text. If they are protected, there is no user interaction with them at all.