People can sign Autograph Book during the game, but signing it once it’s on the battlefield won’t add more page counters.

You can (and should) sign your own Autograph Book to get things rolling.

People can sign anywhere on the card, but each autograph must be distinct so they can be counted.

People can sign Autograph Book more than once, but it’s one page counter per person, not per autograph, so they’re just taking up space where other people could be signing.