All mechanics have the same cost because the dice pools are smaller, the different mods are capped at 3 each, and they interact with pre-Edge and post-Edge differently.
Reroll vs. Adding dice: One mechanic is not twice as good as the other, so if one cost 1, the other cannot cost 2.
Thematically, adding dice is more about aptitude and power while rerolls are more about accuracy and precision, but they basically do the same thing. I am no math wizard but I think rerolls do better with smaller pools/pre-Edge but dice pool increases do better with larger pools/post-Edge. But don't quote me; i don't care enough to figure it out. I just stick with the theme.
An advanced effect, as far as I understand, is anything that does something other than adding/subtracting dice, rerolls, adding damage, reducing damage, or acting upon the narrative. I would imagine knockdowns, stuns, and other such effects.