If you have the new Vibrant4G, the "H" means "HSPA" which is simply put the 4G service. That "H" will change between "3G", "E", "H", and a wireless symbol. It just shows which signal you're getting for data.
As for the home page, you can either just keep hitting back until you get there, or if you're pretty far into browsing just hit the settings button then open a new window and close the other one. I'm not sure if there's an actual "Home" button for the browser if there is I haven't found it yet.
