I'm wondering why you'd want to do this, its not really beneficiary for rankings on search engines.
Anyay, in Flashlight>framework>php>function-set-avia-frontend.php you'll find
if($logo = avia_get_option('logo'))
$logo = "<img src=".$logo." alt='' />";
$logo = "<h1 class='logo'><a href='".home_url('/')."'>".$logo."</a></h1>";
$logo = get_bloginfo('name');
$logo = "<h1 class='logo bg-logo'><a href='".home_url('/')."'>".$logo."</a></h1>";
Here you can add an in "is_home();" statement with the h1's applied and else you'd display it as a span rather than a h1, you might have to adapt the styling though.
The post title thing depends on what page template your homepage is using. Again, it's not advised to do this for SEO purposes, but I'll assume you know what you're doing.
Let me know if this helps :)