I accidentally deleted Google off the favourites 'bar' in the Metro Internet Explorer (the one you can access on start screen) and was wondering if there is any way of getting it back, without a system refresh.
If I'm understanding your question properly, all you need to do is this:
1. Navigate to Google.com
2. Open the address bar by either right-clicking, swiping in from the top or bottom with your finger (touch gesture), or clicking the three dots in the bottom right corner
3. Click the star (favorites) icon
4. Click the star-with-the-plus-sign icon
Ah, I see. That list is very strange... Facebook disappears from there all the time for me. Getting it back usually takes a combination of going to the site a bunch of times in a row, and deleting others on the list that you might not frequent as often. You can do that by right clicking and selecting "remove."
Fire up IE Desktop and do any adding, deleting, moving around there. If you still have issues after that, you have a sync issue up on OneDrive and all your other devices that are associated with your MS account.