Yes, you can raze any structure in the world; your cities as well as cities that are captured.

I believe that the unrest due to an outside occupying force goes down by a certain percentage each turn. Depending on your strategy, you might want to wait out the occupational unrest to make use of the city (it may have a large number of essence slots).

(please correct if I am wrong, anyone).

My best guess is that it's because the magical/elemental damage bypasses the defense stat. So the high defense stats you see later on in the game are completely ignored by a portion of your attack. It's what makes magi so deadly: they do the same damage against a 50 defense unit as against a 0 defense unit (if they have the same amount of resistances of course).

Also - in FE (not LH), lightning hammers had +1 electric damage per level, instead of a flat bonus like the current ones.  So if you're reading older threads, they may be talking about the previous incarnation of the hammers.