Do you gain more experience on higher difficulty levels

With Patch 1.9, yes you can. (without mods or console commands)

Patch 1.9 adds a sixth difficulty level: Legendary. It reduces damage dealt by the player to x0.25 and increases damage taken by the player to x3.

If you want to make the game harder, focus your skill points and perks on non-combat skills: Speech, Pickpocket, Lockpicking, etc. You can also put skill points and perks on combat skills that you won't be using in combat. This will level up your character (which will make enemy level difficulty scale to your level), while at the same time, not make your character stronger for combat.

With the Dragonborn DLC installed, perks may be undone and redistributed at the cost of one dragon soul per skill tree.

At the end of the At the Summit of Apocrypha quest, you will have access to different portals (one for each skill) which allows you to clear and regain any perks in that skill tree, at the cost of one dragon soul. You remove all perks from a single skill perk tree and can use these reclaimed perks on unlocking any perks you wish, including perks taken from said perk tree. By reading the Black Book, Waking Dreams, you can return to Apocrypha and alter the skill trees whenever you wish.

Mods for turning the difficulty up can be found in my answer to the question, "How to make Skyrim more challenging at higher character levels?"

^{Sources:
http://www.uesp.net/wiki/Skyrim:Combat#Difficulty_Level
http://www.uesp.net/wiki/Skyrim:Skill_Perks#Perks
http://www.uesp.net/wiki/Skyrim:Patch#Version_1.9}

Much a like the 'Dismay' shout and the Nord power (which i never used) the 'Howl of Terror' will have an effect throughout every level in the game.

Note that that the spell tome which also has this effect will later have no effect as you level up.

If you wish to boost smithing or any other skill i suggest you do this late on as your combat will be less effective throught higher levels when enemies get stronger. (DONT CHEAT) :)