Yep. Any JAA examiner can sign the paperwork of any other JAA member state - within the privileges of his authorization of course.
No they can't. Some states only allow their own examiners to sign paperwork and others will allow foreign examiners to sign with prior approval.
Spain and Italy as an example wanted copies of my Examiner authority before I was allowed to sign revalidation's and carry out LPC/LST's.
I would suggest that anyone wanting a licence signed by a foreign Examiner contact there own NAA first and check it is OK.