Page-level permissions and groups
If you grant access to a Google Group for a specific page, all the current members of that group will have access to that page at the level you specify unless they already have access to your site or page at a higher level. For example, if you give someone edit access individually, then give view access to a Google Group to which they belong, the person will still have edit access. On the other hand, if you give someone view access individually, then give edit access to a Google Group to which they belong, the person will also have edit access.
If members are later added to a group that has access to your site, those members will have access to the site at the level of access given to that group. If members leave the group, their access level will become whatever level you specified for the public or for their specific email address -- whichever is higher.
For Google Apps users, if the site is editable by the entire domain, then to make a particular page editable by specific set of users, you'll need to change the permissions for that page to private, then add in specific people who you want to be able to edit.
Page-level permissions and public sites
Making your site public can essentially override your page-level permissions.
Visitors to your site will always be granted the highest level of access available to them, even if you've deleted them from a specific page. For example, if you make your site publicly viewable, but delete a specific person from a page, they will still be able to see that page.