Is there any website that provides a service to send MMS (Multi-media
Messenging Service) from country to country? i.e. If my friend was in
the UK and I was in the UAE and they wanted to send me a picture via
MMS would that be possible through a server on the internet? I believe
that it isn't possible to send MMS directly internationally...

It largely depends on the carrier (cell phone service provider) and
how their SMSC works.  MMS is typically delivered via SMS (indicating
a URL that the phone then retrieves for the image/video/sound), and I
have successfully used SMS across international boundaries a great
deal.  Sometimes I can send an MMS message to a co-worker in Europe
and it will arrive moments later, but sometimes it takes a day to
arrive or never appears at all.

Sorry for the lack of definitive answer.

Oops.  I deleted my first paragraph:
Typically the service provider web site has a web page for sending
messages to their customers, but not all of them allow MMS.  I've had
luck with forming my own MMS messages with utilities like mmscomp,
putting them on a web server, and then sending a message via a Now SMS
(ihub.com) MMSC running on a server here.  See
http://www.ihub.com/MMS%20Messages.htm for how we do that.