First question:
Go to
Settings >> General >> Tagline
Make sure this is blank. This is not really a Graphene issue, but a WordPress issue. However, Graphene gives you another way to display this tagline in the title bar. Go to:
Graphene Options >> Display >> Miscellaneous Display Options >> Site Title Options
From there, you can have complete control over what appears in the title bar.
Second question:
Enter the URI for your favicon image here:
Graphene Options >> Display >> Miscellaneous Display Options >> Favicon URL
You may have already figured this out, since I see a favicon there already. (Some hosts will automatically apply a favicon across all subdomains, as well; I don’t know if yours does or not.)