Moving page urls with associated facebook likes

Hi,

Let me start with saying that there exists a site http://www.eaxmple.com and a page with link http://www.example.com/page1.

Current setup:

I had installed wordpress in the root folder.
I had a static home page and several other pages, one theme and few plugins. Just wanted to mention that I had used these two plugins in the pages,
a) Multiple Featured Images
b) Allow PHP in posts and pages,
though it might not be relevant to my question that I am going to ask. So in brief it is a very simply site with one simple but custom theme.

Now after using this site for sometime I want to change the look and feel a bit. But want to keep the old site as is (without changing anything at all) as an archive. Lets say the old site can always be accessed in future by http://www.example.com/old, so the earlier URL of the page1 which was http://www.example.com/page1 now should be http://www.example.com/old/page1

Q1) What is the best way to do this?

One important point that I had a facebook like button in page1 (www.example.com/page1) . I used the following lines in the page.

<div class=”fb-like” data-href=”http://example.com/page1&#8243; data-send=”true” data-layout=”button_count” data-width=”450″ data-show-faces=”false” data-font=”verdana” overflow=”visible”></div>

Q2) Please note that I want the likes that has already been made should remain associated with that page even after this move.

Want to make a note that after moving I might want to create a new page with the URL http://www.example.com/page1 but using a
new theme.

So once I am done moving all the pages from http://www.example.com to http://www.example.com/old I want to create a page http://www.example.com/page1. So http://www.example.com/page1 is the current page and http://www.example.com/old/page1 is the old page and the facebook likes that are currently associated with http://www.example.com/page1 should then be associated to http://www.example.com/old/page1 and the new page http://www.example.com/page1 would start getting likes from zero.

May be I have asked a simple question is a complicated way. Any help is appreciated and feel free to ask me to rephrase this question if needed.

Thanking you as always.