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.
War Caster lets you cast a spell instead of an opportunity attack, which is made just before the creature leaves your reach. If your reach is 5 feet and you use War Caster to cast a ranged spell attack then, yes, the attack is made with disadvantage.
If you have a natural reach greater than 5 feet, then the attack is made when the creature is more than 5 feet away, so this doesn't apply. Similarly, it doesn't apply to melee spell attacks or spells that use saving throws. You are also good if you have the Crossbow Expert feat.
Best Answer
All bonuses to AC stack.
I assume you're thinking of previous versions of D&D, where bonuses of the same type didn't stack. However, in 5e, the majority of ways to gain AC are separate ways to calculate your base AC, such as Plate Armour, which sets your base AC to 18, or Mage Armour, which sets your base AC to 13 + Dex. From the Player's Basic Rules, page 9:
Actual bonuses to AC are very rare in 5e, and stack fully with each other and with different sources of AC, unless the source or the bonus specifies otherwise. An example of this is the Monk's Unarmoured Defense ability, which specifies that it only applies when you are not carrying a shield. Note that it says nothing about the Shield spell, so that would function normally.
An example of non-stacking bonuses is the physical shield itself, which specifies that you can benefit from only one shield at a time. So carrying 2 shields only gets you a +2 bonus. (Player's Basic Rules, pg 44.) Note that the Shield spell provides you with 'an invisible barrier of magical force', not a (lowercase) shield. (Player's Basic Rules, pg 100.) So it does not come under this exception and stacks with a physical shield without difficulty.
So a shield stacks with the Shield spell, and both of them stack with any armour you are wearing, or Mage Armour if you have that instead.