Yes of course, you can create an account as many as possible, but as far as I know, there should be no connection between the two accounts (open for correction if I'm wrong).
For participating in signature campaigns, you are eligible and there's no stop point in doing so. I have an instance to be demonstrated here, I have seen two user goaldigger and ltcbtcdigger both participated in one signature campaign (although, I have no proof that the both accounts are alts). So,  there is no penalty in using your alts to participate in signature campaigns.