Is there a way to embed a business catalyst ecommerce site into another site?

You can do things like this with iframes but not really, not when you going through payment options etc properly. You can send to other sites, new tabs and different domans with similar styles but it will be messy.

You can not fully emebed one site into another though.

Yes you could do it with the API, but it would an epic programming adventure to get it going, as far I know no one else is doing it. It would be extremely slow to use the API in realtime (ie get the contents from the API every page request as the API is slow and times out certain parts of the day sometimes) so you would have to sync your data between the sites. You would also have to work out shipping externally because you can't get any sort of shipping information from the API (as far as I know)

An easier way would be to setup a reverse proxy to your BC site, the only issue with that is that when you start to hit HTTPs pages on checkout you wont be able to proxy them (securely) unless you get your own certificate for the site you are proxying from. I have done this for other sites before but not BC, in theory it should work because BC allows any domain and they shouldn't be any sort of domain / RDNS security checks.

I think what we are saying is you can do this a few ways, But considering it is eCommerce etc - We would not recomend it.

BC will likely do all you did in the site you got currently so you probably should look to port it all in BC.