Does experience gain from damaging Restoration Spells depend on damage dealt

It applies only to attacks with two-handed melee weapons.

If it helps, reread the language as attacks based on your 'two-handed weapon' skill do 13% more damage.

And before you ask, yes, that means it doesn't apply to bows either.

This is a difficult question to answer. This command doesn't show the destruction skill xp number.

GetActorValueInfo DestructionSkillAdvance

In order to determine the skill experience to level, I had to try/(reload after) this command:

advskill destruction 100

Where 100 is the amount of skill experience to gain.

I went Frost Giant tickling. The character had destruction skill 25, firebolt and lightning bolt. Through trial and reload I determined that

1. The character needed 475-480 experience to level destruction to 26.
2. It takes 12 firebolts to gain the needed experience (4 trials, same result each time).
3. It takes 10 lightning bolts to gain the needed experience (4 trials, same result each time).

I only had the Novice And Apprentice perks (no damage increaser perks) for these tests.

Disclaimer, it is possible but unlikely that Frost Giants have a hidden fire resist that reduces damage done and therefore xp gained. (getactorvalueinfo electricresist seems to work on my character, but electricresist, fireresist and frostresist all show 0 for the giant). If frost giants resist fire, then the remainder of this post may be garbage.

OR

Lightning bolts award more xp than fire bolts. This is most likely due to lightning bolt's higher magicka cost.

Lightning bolt's base cost is 51. 9 * 51 = 459 (not enough). 10 * 51 = 510 (level up).

Firebolt's base cost is 41. 11 * 41 = 451 (not enough). 12 * 41 = 492 (level up).

Ice spike's base cost is 48. (did not test)

If you have discounts to the point where you don't worry much about magicka costs... this makes lightning bolt a much better spell to be casting than fire bolt.

So to answer the question... Burn damage doesn't factor into skill gain. Consider a 30 hp critter. If you firebolt them for 25 and burn the remaining 5 hp, you're getting 41 xp (for 41 magicka before discounts). If you lightning bolt them for 25, and again for 25, you're getting 102 xp (for 102 magicka before discounts).