Armor Class as Damage Reduction in 5th Edition
Spells not working as increased Armor Class is a design intent from D&D 5th edition that does not exist in pathfinder, so we have to work around that design. Armor class in general is higher in pathfinder as the levels go on, and so does the attack bonus of players and enemies alike.
In 5th edition, the spells that grant AC instead grant you the equivalent to a specific armor's AC, like Mage Armor granting 13 AC, which is similar to a leather armor. This was designed so Armor Classes will hardly go above 20 even when the character's dexterity bonus is added on it.
Shield of Faith seems to be an exception here, as it still grants a fixed AC bonus.
So, you have two options here:
Accept this design and make it so those spells also grant a specific Armor Class, which will grant damage reduction instead of making you harder to hit, instead of adding on top of your armor class, this way, a character that has a full plate will gain no benefit from mage armor/barkskin cast of them. This sounds closer to the design intent for 5ed spells.
Refuse this design and make those spells actually increase your Defense Score (which acts as the AC for those not familiar with the Armor as Damage Reduction system). This second choice will make those spells stronger than armor (which is something you have to decide if it's intended or not).
The second approach also has the issue of increasing the average AC of a character that has access to those spells, so monsters will be less dangerous to them (they need to roll higher to hit).
In pathfinder, Shield of Faith grants a deflection bonus, one of the strongest bonuses in the game. So, instead of simply adding up to your AC (if i were to convert this) i would make the spell increase your Defense Score.
Resistance and Vulnerability with Damage Reduction
Again, Damage Reduction is a thing that does not exist in D&D 5th edition, but is very common in Pathfinder. There is the feat Heavy Armor Mastery that says:
While you are wearing heavy armor, bludgeoning, piercing, and slashing damage that you take from non magical weapons is reduced by 3.
While this sounds and behave similarly, it is not called damage reduction nor has the other specifics for the rule, unlike on previous editions.
The design choice was to replace Damage Reduction by Vulnerability or Resistance to specific types of damage, and with this, simplify the whole deal with reducing or increasing damage and which applies first.
The main issue is deciding which to apply first:
The designers for 5ed did give us an example on how this should work if that scenario ever happens:
Resistance and then vulnerability are applied after all other modifiers to damage. For example, a creature has Resistance to bludgeoning damage and is hit by an attack that deals 25 bludgeoning damage. The creature is also within a magical aura that reduces all damage by 5. The 25 damage is first reduced by 5 and then halved, so the creature takes 10 damage.
So the best approach here is to not change this design choice and apply the Armor Class's reduction before Resistance/Vulnerability. This will avoid any complications as which should apply first and second and so on.