help recovering SMS's from s3 with broken screen

Hi guys,
I recently managed to launch my phone from my pocket at over 100ft on a fun fair ride - clever. It now boots up, makes the noises when booting and has the blue LED light as expected but the screen is dead.

I think I received a good few text messages while the screen was dead but it was on, and now I have my sim in another old phone (HTC wildfire S) I expected I would see all these unread texts but I do not. I am guessing these texts went to the s3 phone storage?

So I have a few questions:


]Do SMS back up to google accounts automatically? If so how can I recover them to the new phone?

Is there any way of me seeing the unread texts from my s3 through a USB connection to a PC? as it still connects to a computer and I can view the data.

I looked into controlling the screen of the broken s3 from a PC and it seems you need USB debugging turned on and I couldn't figure a way of doing that without the screen being on - anyone know if that is possible?

I also looked at getting a micro USB to HDMI adapter to try contol the screen from a computer, something like this - would that work? Micro USB MHL to HDMI Cable adapter HDTV Samsung Galaxy S3 S III i9300 S4 I9500 | eBay Is that something that could work?

Any advice would be greatly appreciated!


Cheers
Dan

I have managed to back up my messages using 'samsung Kies 3' which creates a 'Message.sme' file, any ideas if there is a way I could view this .sme file on a computer? I have done some research with no luck so far...

Cheers
Dan