Does the damage bonus from Two-Handed-Style apply to spells

The answer to your question, and the answer to your problem are two different things I think.

Damage Reduction seems to not be taken into account when dealing with Damage Over Time effects. I would be more certain of that if I had more than one DoT spell to hurt my team with, but Concelhaut's Corrosive Siphon dealing supposedly Corrosive damage works the same whether my character wears +6 Corrosion DR armor or not.

In Combusting Wounds case... Directly testing it is impossible, it doesn't hurt allies. And however I look at it, the description seems wrong. If it were a DoT effect, we're lacking information about one time - either the time over which that 5 damage is distributed, or time the spell lasts.

What follows is a baseless conjecture

It is possible that this 5 damage gets lost - if it really is DoT it might (extrapolating from my experiences) apply wrong amount of damage, and disappear the reminder if timer is not in the correct by-3-divisivness. Or it might have a long timer (in the realm of 9 seconds, which would be about 2 per 3-second period), and not stack which would fit your experience of unimpressiveness.

Any way I look at it I think we will hear about DoT effects in patch notes sooner or later.

There are two parts of the question, let me start with the easier one - Weapon and Shield Talent. After experimenting it seems that this talent works as advertised with Larder Door as a shield - bonus deflection is added and it does apply to reflex as well.

Now for Two Weapon Style. That one is harder, largely because the game does not provide an interface option to tell how fast an attack is. However I can bypass that through cunning use of cheat tables in CheatEngine.

Two Weapon Style talent modifies property called DualWieldAttackSpeedMultiplier. Every character has it at 1, when the talent is taken it is increased to 1.2. Since that's not very noticeable I volounteered to increase it to 20 just to see what happens. Character wielding normal two weapons was attacking like crazy - and character with a weapon and Larder Shield didn't change it's attack speed (still using normal AttackSpeedMultiplier property).

Therefore Two Weapon Style talent does NOT work with that shield.

As a bonus - Quality enchantments do not increase the damage Larder Door does.