Yes!

All content scales with the level of the character that created the game. This changed in patch 2.0 (the pre-Reaper of Souls content patch).

This patch replaced the existing difficulty system (which did not scale) with a "Monster Power" style difficulty system. This means that as the game host levels up, the overall difficulty of the game rescales to the new level.

This is further clarified by Grimiku, one of the community managers at Blizzard:

So, the Normal > Nightmare > Hell > Inferno progression path is gone. Instead, starting in the pre-expansion patch, you’ll find that monsters will level up as you do, and they’ll gain additional affixes depending on what level range they’re in. You’ll be able to influence monster damage, health, and rewards by selecting one of nine new difficulty settings* as well, similar to the way Monster Power works currently. The result is that you should have a lot more freedom in customizing your level of challenge without worrying about multiple playthroughs of the story to get there.

Channeled spells use up the listed AP cost per "tick". The amount of time each "tick" takes depends on your weapon speed.

So in this case, each "tick" will cost 13 AP (7 less than normal).