It's not possible to add form fields to a signed file, at least not one that has been properly digitally signed. If the signature is just a "wet" drawing or a stamp or something like that then it would be possible, but it's not a "real" digital signature.
To answer your questions:
1. You can set the fields as read-only or flatten the file. Neither one is a real lock, like the one you get with you digitally sign it, though, and will not prevent someone willing and with the proper tools and knowledge to edit it.
2. Yes, both options can be used as a part of an Action in Acrobat Pro.