Since the LiveCycle form did not have "digital signature fields" added when it was designed the existing signature placeholders (they are not form fields) will not be able to be signed regardless of the document security setting for "signing" since the "Modify" is not allowed.
Since you are a consumer of this form and not the author I won't try to go into what should happen to make the form more usable - you should probably fill out the form in Acrobat or Reader, print and then sign with ink on paper. Once signed you could mail or scan the form to email.
Thanks,
Josh