If possible, I'd also like to increase the size of the header and remove the border around it.
To remove the border from the header image, you can add this to your Appearance → Custom Design → CSS page:
#masthead img {
border: none;
}
Coming in the next release of the core WordPress software, there will be a new way to adjust header sizes, but currently the only way to do that is to manually replace the header image with CSS. Here is an example for how to do that in the Forever theme:
First, create the header image with the proper dimensions you'd like to use on your computer, upload it to your media library, and copy down the image URL.
#masthead a img {
display: none;
}
#masthead {
padding-top: 30px;
}
#site-title + a {
display: block;
width: 885px;
height: YOUR_IMAGE_HEIGHT;
background: url(YOUR_IMAGE_URL) no-repeat;
}
Replace YOUR_IMAGE_URL with your image URL, and replace YOUR_IMAGE_HEIGHT with your image height.
Note that whatever value you decrease the height by, you should also decrease the "top" value in the #text-3 block by the same amount if you used the previous example in this thread to move your social media icons.