In employment: To start work, to end work. In unemployment (UK): To sign on to benefits, to sign off benefits. In computing: Log in and Log off
I would say, whichever way your names sound better together. Just because the man's the MAN, doesn't mean his name has to go first. It is most courteous for whoever is signing to put their partner's...
Everybody signs at the bottom ,but the director first , and everybody else below his signature.
because you are basically greeting the person by saying happy birthday.