You can't disable the Quest log. You can make it open using Alt-L and the Blizzard one using L in the Quest page of the Carb Options window.
The fonts are changed on the Font page of the Options window. "Quest List Font" is the one used by the Quest Log, but the description on the right is the standard Blizzard fonts and sizes. You can right click the window title bar or border and increase the scale slider to zoom the whole window up.
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