1) That is since the image is part of the inner part of the module and the module has padding defined below. You can either modify this or use a different module class suffix and stylize it to your liking.
Template.CSS - Line 730
background: #ffffff none repeat scroll 0 0;
2) You can control this in the Template Manager. If you remove the links from the input fields the social icon won't appear on the front page. There is no option to place a phone number.