You should use different aspect ratio for your images that would fit better. We use 1920px by 600px on our theme dem and I think it does look nice. Square images not going to look good with this theme.
Images in slider are displayed in full size and are not cropped or resized once uploaded which means that you will get what you upload.
Add this code to Theme Options - Other - Custom CSS to make theme wider:
Unfortunately, there is no option to add social icons in header for this theme. The closest you can get is to add them on top of sidebar or create menu item with dropdown with those menu items in dropdown pointing to social networks.
It would look something like this: