I think your map acts the way it does because of the way you have it set up.
Here is a screen shot of my Map Minimap options page:
You will notice that I don't have the option checked to use the Carbonite Button Window. I use
Minimap Button Frame for my minimap buttons. I feel it is more flexible than the Carbonite button window.
Here is a screen shot of my Carbonite minimized map while I'm in Maraudon:
I think the quest giver and turn in icons are shown on the Carbonite map by default when Carbonite is installed (at least I don't remember ever having to do anything to have them show on the Carbonite map). Try checking the "Modules" page of Carbonites options and make sure the "Quest" module is enabled.
One other thing I noticed: Your Carbonite minimized map is set up to be "landscape" (rectangular) shaped. It does look nice that way, but please be aware that, apparently, the Blizzard minimap can only be made to be square while it is integrated with the Carbonite map. The Blizzard minimap will (in my opinion) never cover the entire Carbonite minimized map while it (the Carbonite map) is rectangular.
You might, also, want to go to your "
Path to your WoW folder\Interface\AddOns\Carbonite\" folder and read through the "CarboniteReadMe.txt" plain text file. It will tell you quite a bit about what Carbonite does, and also give you quite a bit of information about how it can be set up. unfortunately, that file is still one of Carbonites "best kept secrets".