Hi,
I'll try and answer some of your questions …
Yes, in order for your users to use GoogleDocs to edit checked out documents they will have to also have a Google account. By default it will be assumed that a users Google account id is their email address, unless a users Google account information has been added to a users account profile.
When a document is checked out from a Site all the users that have editing writes within that site on that document will have edit capabilities on the shared document, those with view will only have view. So you don't need to do any additional configuration, the users and permissions you have set up in your Share site should behave naturally with the way the checked out GoogleDoc is shared.
Cheers,
Roy