[RPG] I’m having difficulty understanding the price of magic arms and armor special abilities

You're misusing the guidelines.

First, let's take a look at what the Pathfinder Magic Item Gold Piece Values section has to say on this issue. Turns out, it is specifically addressed.

The correct way to price an item is by comparing its abilities to similar items (see Magic Item Gold Piece Values), and only if there are no similar items should you use the pricing formulas to determine an approximate price for the item. If you discover a loophole that allows an item to have an ability for a much lower price than is given for a comparable item, the GM should require using the price of the item, as that is the standard cost for such an effect. Most of these loopholes stem from trying to get unlimited uses per day of a spell effect from the "command word" or "use-activated or continuous" lines of Table: Estimating Magic Item Gold Piece Values.

Emphasis mine. It then goes on to take Mage Armor as an example of this:

Patrick's wizard wants to create bracers with a continuous mage armor ability, granting the wearer a +4 armor bonus to AC. The formula indicates this would cost 2,000 gp (spell level 1, caster level 1). Jessica reminds him that bracers of armor +4 are priced at 16,000 gp and Patrick's bracers should have that price as well. Patrick agrees, and because he only has 2,000 gp to spend, he decides to spend 1,000 gp of that to craft bracers of armor +1 using the standard bracer prices.

So yes, your Amulet of Mage Armor and Shield is a textbook example of the guidelines gone bad.

This is understandable. The guidelines are famously weak, often breaking with casual use, as you have encountered. This precise case, however, was anticipated and addressed.

Enhancement bonus is clearly seperated from other magical effects on equipment. Therefore, when Damaging Objects specifies 'enhancement bonus' and not 'effective enhancement bonus', it is implicitly stating that only the base enhancement bonus provides an item more Hardness and HP.

To put it another way, a +2 Longsword makes the weapon simply better than it was, whereas a +1 Flaming Longsword would just add the ability to deal Fire damage. Adding the ability to deal Fire damage does not make the weapon more durable or sharp, which is what an enhancement bonus 'represents'.

From Damaging Objects

Each +1 of enhancement bonus adds 2 to the hardness of armor, a weapon, or a shield, and +10 to the item's hit points.

And from Common Terms

An enhancement bonus represents an increase in the sturdiness and/or effectiveness of armor or natural armor, or the effectiveness of a weapon, or a general bonus to an ability score.

Finally, from Magic Armor

In addition to an enhancement bonus, armor may have special abilities... cannot have an effective bonus (enhancement plus special ability bonus equivalents, including those from character abilities and spells) higher than +10. A suit of armor with a special ability must also have at least a +1 enhancement bonus.

All emphasis mine. The most incriminating line is the bold from the third link, clearly stating that 'Special abilities' are not part of the 'enhancement bonus'.