After presenting Amy with the Relationship Agreement, Sheldon gives her time to read it while he sets up his notary stamp. Notarization by a party to a contract would be ineffectual, so there would be no point in his doing so.
Sheldon states people cannot be owned as property since 1863 when Abe Lincoln freed the slaves, however the slaves in border states were not freed until the thirteenth amendment was ratified in 1865 and, did not take into effect until after Lincoln was killed.
When Sheldon knocks the first time on Penny's door, she immediately shouts "Who do we love?" anticipating that he will say "Penny". However, after the first knock and before he says her name, she has no way of knowing that Sheldon is there or that her name will be called.