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
Therefore Two Weapon Style talent does NOT work with that shield.
As a bonus - Quality enchantments do not increase the damage Larder Door does.