Hi,
#1 seems to be a bug… if you want to hide the title in the sidebar, use custom CSS in Theme options:
header.sidebar-heading { display:none;}
#2 You could make a specific CSS rule for mobile devices (like reducing the font size), but you’re probably better of reducing the size of the site title. If you really want to increase the height of the navbar, just use custom CSS again. Style it with:
header#masthead { height: ???px;}