What you can do is at least match the members in each group.
That should give who is in both groups
The above should give those group members who liked a specific page.
The feature needs to be rolled out to the group you would like to join as well as the page you would like to join.
(I don't believe it's 100% rolled out to everyone)
In addition, the admin must enable it in the group settings.
Once, that's done, you should be given the option.
Ok, it's possible and this is how to do it. Everytime you want to add a second, third, etc page as administrator, you go to that Facebook page, then to the groups tab, then you click in "link your group" and then from the list of groups you are an admin of, and you select the group you want your page to be admin of (a group which supposedly already have one ...
No, Facebook does not archive the posts but for your purposes they may as well be archived.
Facebook uses infinite paging. In order to see older posts you have to page down and down and down until your browser cache sucks up all your available memory and crashes your computer.
Buy more memory and a weight to put on the page down key
Write a ...