Sometimes, but you do realise that the changes will invalidate the first signature? The second signature would apply to all: original and changes.
Yes you can with restrictions. You need to create your original PDF in such a way that you may make certain changes after it is signed. The easiest way to do it is to certify the original PDF with certain permissions. Acrobat Pro UI provides certain combinations of such permissions. Adobe LiveCycle provides more granular combinations of permissions but this is an expensive solution. Try first what Acrobat Pro UI gives you and see if it gets you want you need. You may apply as many modifications and signatures to the document as long as they conform to the certification permissions. The last signer can also lock his signature which disallows further modifications and signing.
If you are using predefined sigfields for signing forms ... yes
Because you can define for each sigfield WHICH fields should be locked ( == also be signed ), the sigfields for the initial signing of the empty form should not lock any fields except the sigfield itself.
The sigfield(s) after "filling" the form fields should lock the form fields. You even can define which fields should be locked by which sigfield. This enables even "section" signing (e.g. a group of form fields).