Yes.
Bonuses in 5e are rare, and we don't know all of the details yet, but there is no reason to think that Mage Armor and Shield do not stack. The only thing we really know is that casting a new concentration spell breaks the previous one. Neither of these spells are concentration spells and thusly they would not conflict in that way.
5e does not use named bonuses as far as we can tell (preferring Advantage most times other editions would use a named bonus), and really Mage Armor is not a bonus, it's a set amount of AC. The key point on these two spells is that Mage Armor affects your base AC whereas Shield is a bonus to your AC. In this case there is no potential conflict between the spells as far as bonus/base rules go.
The other potential source of conflict would be if two spells did not stack. Thankfully the basic rules have us covered there:
The effects of different spells add together while
the durations of those spells overlap. The effects of
the same spell cast multiple times don’t combine,
however. Instead, the most potent effect—such as the
highest bonus—from those castings applies while their
durations overlap. (Basic D&D p 81)
Since Shield and Mage Armor aren't the same spell their effects can overlap just fine.
So yes, they stack.
Caveat: again, we don't have the full PHB and DMG yet so there may be bonus stacking rules outlined in those volumes that are not yet a part of Basic D&D (I've just done a search). There are limited rules on bonus stacking so I'd assume that all bonuses stack for now. The only exception is proficiency where we have clear rules on the subject (it can be multiplied and divided, but never stacked). Proficiency is the only bonus stacking ruling given in Basic.
You are almost exactly correct.
All the math you have is accurate. However, you've missed a subtle rule mentioned in the PHB (pg. 202) regarding spells cast as Bonus Actions. Namely, when casting a spell as a bonus action
You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.
Thus, while it is possible to reach 27 AC using the methods you've described, you cannot cast Haste and Shield of Faith on a single turn.
Best Answer
In Pathfinder, bonuses of the same type do not stack.
Mage Armor and regular armor (full plate, etc.) both provide an armor bonus, so they do not stack. The same can be said for a shield and the spell Shield — they both apply a shield bonus to AC. When they don't stack, you use the higher of the two bonuses.
This means that Shield and Mage Armor do stack, because they provide bonuses of different types — Mage Armor grants an armor bonus and Shield grants a shield bonus.