Paul,
Yes, you can get your posts and (I believe) have the Like button associated with that post show on your page. I'll give the steps and recommendations below, but definitely let us know if you have any questions, issues, or feedback.
First, I'd honestly recommend making the post on your Facebook profile and then simply make an HTML representation of that post on your site. It is possible to 'pull' the actual post into your site and display it there, but unless you plan to do this frequently or for every post (so that it's automated), that's just getting in over your head..
So, let's say you've created a Facebook Post to your Page and then created an article on your site with the same text (or modified however you want). Next:
* Go to
developers.facebook.com/tools/explorer
* In the "GET" box, add <YOUR_PAGE>/feed to the URL, so it will look like:
https://graph.facebook.com/SourceCoast/feed
That will show the recent feed posts to your Page. In there, you'll be able to find your recent post (look for the "message" variable" and then, under that, will be a Like and Comment link. I *believe* you can use those links in the {JFBCLike href=<LINK>} and {JFBCComments href=<COMMENT>} tags.
Obviously you'll have to test (a lot), but I think that should be all you need. If you decide you need to automate the fetching of that stuff, you can see from the Graph Explorer that it should all be available to you (the message, the links, etc)... it will just take a bit more work to do that, and if you don't want it automated, that's not worth it.
Let us know if that helps, and good luck!
Alex