Difference between a page and a group on Facebook?

[myself]

On a Facebook page, you are the only person who can post. people can only like, share or comment. On a Facebook group, you are not the only person who send posts, other users whom are members of that group, can post, too. The difference between page and group is in the posting and the management of the environment.

Yes. Users can see the admin of the group.

To add more, a group is a place to discuss and is more subject-driven place. For example, if the group is about trading, you will find topics only about trading, not other things. The same goes for the page.