I know its possible to turn off all quest trackers, but is it possible to actually disable the Map? I'd like to be able to roam around Skyrim and
find my way around through memory and reading signs. I know, I could just not look at the map, but there's always the temptation to look
and I was much rather just turn it off all together.

Does anyone know if this will be an option? Or maybe a possible, easy mod that will be made?

why would you want to disable the map you could just not use it, you can disable all the HUD

you could set your key to a certain button and then just rip that key off the keyboard

Un-keybind your map key.

Is the map not sectioned with the quests anymore? I haven't looked in-depth at the interface yet, so I'm not sure whether it has its own window or if its shared, like in Oblivion.

No the quests and stats have been moved to the pause menu.